This week, we're starting a month-long series on marriage. For those in our congregation who are married, I hope that it will be a series that helps us to work through what it means to live as pprentices of Jesus in our marriages. For those who are not married, or who have been married in the ast, I hope that this series will help us understandthat we can live as apprentices of Jesus whatever our marital status.
Life in this world of sin and selfishness, as anyone can attest, is complicated. Marriages are no exception to this. Consider, for instance the marriage of Jacob and Leah (oh, and Rachel too! See: complicated!) in Genesis 29. We have to ask ourselves if it is even possible for one mere human to ever fully satisfy another. If not, then how can we live "complete" lives?
Even in our churches, we often focus all of our energy and attention on those who are married. I can testify from my pre-married days of often feeling left out and less than those around me. Once, many years ago, I remember visiting a church which explicitly stated that only married couples were allowed to run bible study groups.
We live in a hyper-sexualised age. Much of our advertising relies on this. Many of the movies, books, and celebrities we fill our lives with suggest that an ultimate aim in life is to find the one that can fulfill you in all areas.Many people don't get married these days, preferring instead to simply co-habit with someone. At first glance, this makes sense: they have found someone who loves them and who makes them feel special. But on deeper reflection, this represents an unwillingness to publicly and permanently throw one's lot in with another. To co-habit with someone other than your spouse is to keep one's options open into the future.
Lest those who are married get uppity, it must be said that sometimes, cohabiting partners could be seen as more honest than people who get married, only to later divorced. The difference between a divorce and a defacto relationship coming apart is simply that the married couple had publicly committed and bound themselves to their spouse. As far as God is concerned, any time a man and a woman come together, they become one flesh. (See 1 Cor 6:16).
But what, we have to ask ourselves, is God's purpose and design for such a coming together? If God is King, then all of our lives should be centered on him – including our relationships and sexuality. If we think that God's will should be done on earth as it is in heaven, then we should certainly be asking ourselves what God's will is for marriage!
This week, our passage finds Jesus being approached by some religious experts trying to trap him with respect to his views on divorce. In that day, there were two main schools of Jewish thought on this. The first argued that a man could divorce his wife for whatever reason, even trivial ones. Taken to extremes, one could argue that simply being attracted to another woman was a good reason to divorce your current wife! The second main school of thought was much stricter, allowing divorce only in the case of infidelity.
In answering their question, Jesus takes us back to the origins of marriage: the stories of creation and the first couple. Drawing from God's creative intent, Jesus argues that divorce is by nature contrary to God's will. From that same source, we also learn about the God's intended shape for marriage: a life-long commitment whereby a man and a woman are joined together by God into one flesh.
But how do we apply this ideal to the real world messiness of life and relationships today?


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As I get back into the swing of things after a spell of being unwell I wanted a project which was quick and easy, and so I reached for the February Card Kit from Simon Says Stamp. The great thing about card kits is that so much of the work has been done for you. The stamps coordinate with the patterned papers as does the card stock which makes it so easy to put everything together. I've linked all supplies at the end of this post. Compensated affiliate links used where possible at no cost to you.
The Love Always stamp set from the kit has several gorgeous florals and a sweet bird too. The images are very detailed with shading and lots of detailed line work, and although I contemplated colouring the flowers in some way, I felt the amount of detail included would look lovely simply stamped in black on kraft and letting all the detail be the focal point.
I dug around in the kit and found the Neenah Desert Storm card, a couple of Authentique patterned papers and a black pre-scored notecard and started to plan what I had in mind. I picked one of the floral sprigs to use and then trimmed the pieces of card and paper to size. I planned to have the floral image stamped in the top third of the card on kraft card and then have the remaining front panel made up of the red patterned paper with a border along one edge of the black striped paper.
I placed the Neenah Desert Storm piece I'd cut to be slightly smaller than the A2 black notecard in the Mini Misti and used the red piece of patterned paper as a guide as to where to centre the flower image. I closed the door of the Misti to pick up the stamp and then inked it in Versafine Onyx Black ink. This is a great ink for stamping fine details, and I always get a good impression the first time. I added a strip of Gina K glue runner along the back of the red patterned paper and then adhered the black stripe paper. I trimmed the piece to size and then added more glue runner on the back before adhering to the kraft piece.
As this card has quite a vintage feel, I thought a little stitching would add a nice accent, and so I dug out my little sewing machine. This used to belong to my grandmother and is still going strong despite being made in the 1930s or something. I have the original manual tucked away, and it has the factory check date stamped in it. I love using it and the memories it brings back of my Nan. I ran a simple zig-zag stitch over the intersection between the two patterned papers and then pulled the loose threads onto the back of the kraft panel, kept them in place with pieces of washi and trimmed away the excess. I added foam adhesive to the back of the panel and then adhered to the front of the black pre-scored A2 notecard.
For the sentiment, I pulled out the Love Always set again and chose the 'You Are My Soulmate' greeting. I cut a piece of Ivory card from that included in the Card Kit and placed it in the Mini Misti, treated it with an anti-static powder bag to prevent embossing powder randomly sticking everywhere and then stamped in clear embossing ink before sprinkling with Antique Gold embossing powder and heat setting. I trimmed the piece to a skinny banner with a clear ruler and scalpel and then to give it a more aged appearance to fit with the rest of the card, I used a Picket Fence Blender Brush and Stone Ink from Simon Says Stamp and lightly rubbed the strip until it took on a more vintage look. I added the greeting to the card with foam adhesive and used a T square ruler to ensure I had it on straight. As a final accent, I added a trio of gold sequins around the sentiment strip and kept them in place with Gina K Connect glue.
This is really beautiful. Well done!
This is a beautiful card Debby. I keep wondering if I should subscribe to the card kits. Last year there were two or three that I wasn't sure about.
Glad you are feeling better but I thought I heared still a bit of cold in your voice, hope you are completely well soon. So double thanks for this awesome card. Love the colours together. Great that you sill use the sewing machine of your grandmother, they made everything so strong in those days.
Debby, I'm so sorry you've been so unwell… making this beautiful card must have made you feel better, right? So gorgeous… I'm so glad you didn't color that gorgeous bouquet!!
A lovely card Debby, it has never occurred to me to NOT colour the flowers but it looks great!
Beautiful card and great use of patterned paper.
Just lovely Debby! I hope you feel better soon. My entire family here in San Francisco has had something or other since the beginning of the year. We are finally coming back to good health. Feeling grateful.
Great card. Sorry you were ill . Glad you are starting to feel better. Keep getting better.


text:
Grizzlies announce addition of ex-Timberwolves guard Jones
Memphis Grizzlies announce they've signed restricted free-agent guard Tyus Jones
Written by The Associated Press
MEMPHIS, Tenn. (AP) — The Memphis Grizzlies have officially announced that they've added guard Tyus Jones, a restricted free agent who played for the Minnesota Timberwolves last season.
The Timberwolves already had issued a statement late Tuesday night wishing Jones luck in Memphis, an indication they didn't plan to match the Grizzlies' offer sheet to him. The Grizzlies didn't make a formal announcement until issuing their own release Thursday night.
Terms of the deal weren't disclosed, but ESPN has reported that the Grizzlies had given Jones a three-year offer sheet worth $28 million.
Jones averaged 6.9 points, 4.8 assists, 1.2 steals and 22.9 minutes for Minnesota last season. The 23-year-old set an NBA single-season record with a 6.96 assist-turnover ratio.
Jones, who is 6-foot-2, will wear No. 21 for the Grizzlies.
More AP NBA: https://apnews.com/NBA and https://twitter.com/AP_Sports
Letter: People on left doth protest too much
Letter: Keep migrants out until we have room
Global shares mixed in lackluster trading, Nikkei falls 0.7%

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}
The theory of the anomalous Hall Effect (AHE) has a long history
The appearance of the Hall current requires breaking of some basic symmetries.
It was proposed by Karplus and Luttinger in early 50s \cite{Lutt} that the anomalous Hall effect in ferromagnets results from the interplay
 of the exchange field, which breaks the time-reversal symmetry, and the
spin-orbit coupling, that violates the chiral symmetry. Interestingly, at the same time a similar effect was
predicted and explained in geometrical optics \cite{Fedorov}, however, its relation to the
AHE was revealed only recently \cite{{Onoda},{Bliokh}} after the modern interpretation of both effects in terms of the Berry phase, which affects the motion of wave packets, had been constructed.\cite{Jungwirth,Niu,Zeldovich} Luttinger \cite{Luttinger} built a detailed theory
of the AHE based on the high order quantum Boltzmann equation calculations.\cite{Kohn}  In that work Luttinger identified various contributions, known today
as Berry phase contribution, the skew scattering, the side jump on the impurity potential and a contribution that involves interference from many scatterers.

Since then, a number of theoretical works appeared that extended the theory. However untill recent time
most  of them had been devoted to what is today called the extrinsic AHE. In the extrinsic AHE a simple Bloch band structure of the system is assumed and the spin orbit interaction is
localized on the impurity potential via terms of the form $\lambda_{SO}\hat{\sigma}_z  {\bf \hat{z}}{\bf k \times \nabla}V_{dis}(x)$ e.t.c. It was recognized by
 Smit, Berger and others
\cite{{Smit},{Berger1},{Berger2},{Berger3},{Bruno-Dirac},{Extrinsic1},{Extrinsic2}} that in this case the main contributions to
 the Hall current will be those from impurities via the side jump and the skew scattering mechanisms.
In contrast to the extrinsic AHE, the intrinsic one assumes that the spin orbit coupling is already present in the band structure of the system
and generally cannot be considered as weak in comparison even with the Fermi energy. Recently the interest toward the intrinsic AHE has grown up
considerably due to new applications in the diluted magnetic semiconductors (DMS) and due to the interesting modern interpretation of the Hall current
in terms of the Berry phase.\cite{{Jungwirth},{Fang}} The Berry phase contribution to the Hall current was shown
to be in good quantitative agreement with experiment in many different materials with strong
spin-orbit couping in their band structure, giving weight to the theory involving this contribution alone. \cite{{Fang},{Experiment1},{numerics1}}

The Luttinger's theory of the intrinsic AHE, however, predicts that other contributions should arise due to the scattering from
 a disordered potential even  if the disorder potential itself is spin independent. The asymmetry in scatterings  becomes transparent
 in the basis related to the Bloch states.
As an example, Luttinger considered a rather simplified model which demonstrated that such corrections must reverse the sign of the Hall current in the dc-limit, in comparison to the clean limit, though in the high frequency AC-case the clean limit contribution should dominate.
The same results have been shown by several other works utilizing different approaches and focusing on this simplified model.\cite{{Adams},{Nozieres},{Chazalviel}}

The results from these simplified models seem to be in a contradiction with recent work which did not find such a change of sign in
numerical simulations or in a comparison with the experimental results.  We show here that a possible resolution of this discrepancy is the simplicity of the early models from which many generalizations were stated without justification and whose results depended drastically on the simple momentum depencence of the Berry curvature of the Bloch states.

The work by Luttinger and works of other authors, related to the disorder contribution to the AHE,
are rather involved. Generally various contributions separately
turned out to be not gauge invariant and only the final result was physically meaningful.
Because of these shortcomings, we reformulate the  basic arguments of the previous authors in terms of wave packet dyanamic equations which are
fully gauge invariant and consistent with prior results.\cite{Niu}
Being gauge invariant, the wave packet equations allow one to identify the physical meaning of various contributions. We should note, however, that the wave packet equations are valid only in the limit of smooth potentials. This restricts the applicability of our conclusions and generalizations
of our results should not be made to regimes where the semi-classical treatment is not justified
without careful checks; therefore we did not make the goal to construct the final theory of
the disorder in the AHE but rather to construct a simple formalism that demonstrates basic features
of the problem and highlights a basic key ingredient missed by prior theories studying the effects
of disorder, namely the importance of the momentum dependence of the Berry curvature.

We have found that the change of the sign of the Hall current due to the disorder,
found in the early works, is not universal and arises in the models where  bands have a
constant Berry curvature in the momentum space.
In diluted magnetic semiconductors the Berry curvature is strongly momentum dependent.
This separates parametrically the clean contribution from the others and makes the
sign reversal not universal. Rather generally we find the same sign of the total Hall current
for realistic bands except in extreme situations where one of the bands becomes depleted.

We organize the rest of the paper as follows. In Sec. II we review the wave packet dynamics theory
of Sundaram and Niu \cite{Niu}. In Sec. III we analyze the model for constant Berry curvature
obtaining in a physically clear way the reversal of the sign in the presence of smooth disorder.
In Sec. IV we apply the theory to the case of the Rashba model and show the non-trivial dependence
of the contributions from disorder scattering and the clean Berry phase contribution as a function
of the Fermi energy and in Sec. V we present our conclusions.

\section{The wave packet equations}
The motion of wave packets formed by Bloch states is governed by the following equations.\cite{Niu}
\begin{equation}
\frac{d}{dt} {\bf k}=e {\bf E} - {\bf \nabla}V({\bf r}) \label{dkx1}
\end{equation}%
\begin{equation}
\frac{d}{dt}{\bf r}=\frac{\partial \epsilon ({\bf k})}{\partial {\bf k}} - \frac{d {\bf k}}{dt}\times {\bf F}
\label{om1}
\end{equation}%
where $\epsilon (\bf{k})$ is the energy dispersion in the band, ${\bf E}$
 is the external electric field acting on a wave packet having the electric charge $e$, $V({\bf r})$ is the local potential
in the sample, for example the potential of impurities and
 ${\bf F}$ is the Berry curvature of the Bloch band. For the two-dimentional motion only the out of plane component of $\bf{F}$ is nonzero

\begin{equation}
F_{z}=2Im\left\langle \frac{\partial u^{s}}{\partial k_{y}}|\frac{%
\partial u^{s}}{\partial k_{x}}\right\rangle  \label{adi2}
\end{equation}%
here $\left\vert u^{s}\right\rangle$ is the Bloch state in the absence of the
electric field and impurities and $s$ is the index of the band.

The second term in (\ref{om1}) is responsible for the so called anomalous velocity. For the reader not familiar with the notion of the anomalous velocity
we provide the appendix with a simple example from classical physics that gives an intuitive explanation of the physical meaning of the anomalous
velocity in Rashba coupled 2DEG. For the rigorous theory we refer to the original papers \cite{Niu}.

The anomalous velocity is orthogonal to the direction of
the electric field \cite{{Lutt},{Wannier}} (which we chose to be along the $x$-axes).
\begin{equation}
v_{y}^{(a)}=F_{z}\frac{dk_x}{dt}  \label{adi1}
\end{equation}%

The semiclassical equations (\ref{dkx1}) and (\ref{om1}) map the quantum mechanical problem to a classical one where particles have
the electric charge $e$ and move according to equations of the wave packet dynamics.
We assume that at equilibrium the distribution of such classical particles is the same as the Dirac distribution of electrons in the sample.
This mapping to a classical system considerably simplifies the treatment of the problem both analytically and numerically. Analytically,
one can apply the classical Boltzmann equation approach to calculate the transport coefficients, numerically the molecular dynamics
 simulation of the motion of classical particles is simple  and may not be restricted to a small system size as, for example, in the case of a numerical diagonalization
of a quantum mechanical Hamiltonian.

 Unfortunately equations  (\ref{dkx1}) and (\ref{om1}) are valid in the adiabatic limit only.
They cannot be applied to the case of scatterings on a short range delta-function like potential.
 Only scatterings on impurities, whose potential varies
appreciably only on distances much larger than the size of the wave packet can be calculated this way \cite{Niu}.
In spite of this restriction of its applicability  the limit of a smooth potential is a very interesting one
to investigate the influence of disorder on the anomalous Hall effect.
In realistic applications a system with long range impurities
is realized, for example, in the high mobility 2D
electron gas \cite{Aleiner} and the out of plane Zeeman field can be induced there by polarizing nuclear spins or by introducing additional magnetic impurities.

Recently another related effect, namely the intrinsic spin Hall effect,
was introduced \cite{SHE}. A number of theoretical papers have explored the importance of the disorder.  The debates on this topic are ongoing  (see e.g. \cite{{Inoue},{Kentaro},{Halperin}}).
Understanding the AHE may shed light on the disorder role in the spin Hall effect.

\section{Constant Berry curvature}
\subsection{Clean limit}
In many recent applications the Berry curvature ${\bf F}$ strongly depends on the momentum of the wave packet $k$. \cite{{Jungwirth},{numerics1},{Dimi}}
However,
it is instructive to consider first the one Bloch band 2D system with a constant Berry curvature $F_z$.

For a constant $F_z$ the anomalous velocity (\ref{adi1})
leads to the following contribution to the Hall current
from the unperturbed part of the distribution function in a single band at zero temperature:
\begin{eqnarray}
&&J_{yx}^{(clean)}=e \int d^2 {\bf k} f_0({\bf k}) v_y^{(a)}=\nonumber\\
&=&e\int_0^{k_F}kdk \int _0^{2\pi} \frac{d\phi}{(2 \pi) ^2} eE_xF_z= \frac{e^2E_xF_z k_F^2}{4\pi}
\label{F1}
\end{eqnarray}
where $ f_0({\bf k})$ is the equilibrium distribution function and $k_F$ is the Fermi momentum. The upper index $(clean)$ means that the quantity is calculated in the absence of disorder and the
distribution function of the wave packets coincides with the one in equilibrium at $E_x=0$.

  The case of a constant $F_z$ is realized in the conducting bands
  whose states are weakly hybridized with the states in the valent hole bands \cite{Nozieres} where the spin orbit coupling is allowed.
 If the kinetic energies of electrons in the conducting band are much smaller than the gap between conducting
  and valent zones, the Berry curvature due to such an induced spin orbit coupling can be considered as a constant for all conducting electrons.
  In modern applications it can be realized in some limiting situations, like in the case of R2DEG at a strong Zeeman field (see following sections).
  In this section we show that for smooth impurity potentials
  the wave packet approach easily reproduces the sign reversal of the Hall current when $F_z=const$. In comparison to previous works, however,
  our approach keeps the derivation  gauge invariant and hence is physically clear.

\subsection{Effects of disorder}

  According to (\ref{F1}) if the distribution function is the same as in the equilibrium at zero external field  a Hall current appears
  in the external field  due to
  the anomalous velocity. However, in the steady state the distribution function is no longer $f_0 ( {\bf k})$.
  In the electric field and on time scales much larger than
  the scattering time particles diffuse with a constant velocity rather than accelerate as in the absolutely clean case.
 The anomalous velocity and hence the clean contribution to the Hall current are proportional to the acceleration $\dot{k}_x$. Since in the
 steady state the average acceleration is zero up to the first order in external electric field $E_x$ one can expect that disorder should
 strongly influence the Hall current.

 A natural way to study the effect of disorder on the transport in our case is the classical Boltzmann equation. There is however a complication
 when both nonzero Berry curvature and  finite sizes of impurities must be considered. At a scattering on an impurity potential not only the
 momentum but
 also the coordinate of a particle changes. Usually such a coordinate shift at the scattering is discarded since after averaging
 over many scatterings such random shifts cancel each other and only the changes of the momentum matters. However when the Berry curvature is nonzero
 the additional (anomalous) shift does not disappear after the averaging. To see this,
suppose that the term with the Berry curvature $F_z$ in Eq. (\ref{om1})
is small in comparison with the first one and calculate the corresponding correction
 to the shift of the particle during the scattering on an impurity. Integrating  (\ref{om1})
 over the time interval at which  a particle feels the impurity potential during a single scattering and treating the second term in (\ref{om1})
  as a small
perturbation one can find that, after the scattering, a particle makes an additional shift
\begin{equation}
\Delta {\bf r}({\bf k}, {\bf k^{\prime }})=
{\bf z} \times ({\bf k}^{'}-{\bf k}) F_{z} + \int_{t_1}^{t_2}
\frac{\partial \epsilon}{\partial {\bf k}} dt
\label{zse}
\end{equation}
here ${\bf k}^{\prime }$ and ${\bf k}$ are momentums respectively after and before the scattering, $t_1$ and $t_2$ are times of entering and leaving
the impurity in a semiclassical picture.
The second term in the rhs. of (\ref{zse}) is just the shift due to the normal velocity. To first order in $F_z$ and
${\bf \nabla} V$ it is not affected by the Berry
phase and hence is averaged to zero after many scatterings; therefore we will disregard it in our
future discussion.

The particle's displacement due to the first term in (\ref{zse}) is due to the
anomalous velocity.
This shift does not depend explicitly on the details of the impurity potential and does not have the chiral symmetry.
There are two main rather distinct effects due to the appearance of this anomalous shift.
The first effect, the so called side-jump,
is that the $y$-component of this shift does not cancel after the averaging over many scatterings and thus contributes to the drift velocity perpendicular to the electric field, i.e. to the Hall current.
We will focus on this effect in the following subsection.
The second effect is that when a scattering takes place in the presence of an external electric
field there is a change in the potential energy upon a scattering given by
\begin{equation}
\Delta U=-eE_x\Delta x  \label{b1}
\end{equation}%
where $\Delta x$ is the  shift along the external electric field.\cite{{Berger1},{Berger2},{Berger3}}
Both of these effects, as shown below and in the next subsection, give the same contribution as
Eq. (\ref{F1}) but with an opposite sign in the particular case of a momentum-independent Berry curvature.
Because both contributions are linear in $E_x$ we are able to consider them separetly when considering
the linear response of the system.

Let us focus first on the second effect. Here only the anomalous part of this
shift is important for Hall current calculations
\begin{equation}
\Delta x=-F_{z}(k_{y}^{\prime }-k_{y})  \label{b2}
\end{equation}
and the effect of the normal part of the shift only renormalizes the diagonal current response to $E_x$. Since the
total energy remains the same after an elastic scattering, the kinetic energy
must change by the amount
\begin{equation}
\Delta \epsilon ({\bf k},{\bf k^{\prime}})  = \epsilon ({\bf k^{\prime }})-\epsilon ({\bf k})=eE_x\Delta x
\label{b55}
\end{equation}

This effect leads to an instability of the initial equilibrium distribution
function $f_{0}({\bf k})=f_0(\epsilon({\bf k}))$ due to scatterings.
The Boltzmann equation  is given by
\begin{equation}
\frac{\partial f}{\partial t}=-\sum_{\bf k^{\prime }}\omega ({\bf k,k^{\prime
}})[ f \left(\epsilon ({\bf k}) \right) -f\left(\epsilon ({\bf k^{\prime }})\right) ]  \label{b3}
\end{equation}%
where $\omega ({\bf k,k^{\prime
}})$ is the scattering rate.
Kinetic energies before and after a scattering do not coincide but the difference between them is small.
Since we are seeking a contribution linear in $E_x$ we can substitute $f$ by $f_{0}$ which
depends only on the kinetic energy $\epsilon ({\bf k})$ so we can expand
\begin{equation}
\begin{array}{l}
f_{0}(\epsilon ({\bf k}))-f_{0}(\epsilon ({\bf k^{\prime
}}))= \\
\\
=\frac{-df_{0}}{d\epsilon }(\epsilon ({\bf k^{\prime }})-\epsilon ({\bf k}))=-\frac{%
df_{0}}{d\epsilon }eE_xF_{z}(k_{y}-k_{y}^{\prime })%
\end{array}
\label{b4}
\end{equation}%
This yields
\begin{equation}
\frac{\partial f}{\partial t}=-\sum_{\bf k^{\prime }}\omega ({\bf k,k^{\prime }})\frac{%
-df_{0}}{d\epsilon }eEF_{z}(k_{y}-k_{y}^{\prime })\neq 0  \label{b5}
\end{equation}%
The distribution function will relax until a contribution to it
compensates this relaxation in the stationary limit.

To find the new equilibrium distribution one should substitute $f({\bf k}) = f_0 (\epsilon  ({\bf k})) + g_{E}({\bf k})$ into the rhs. of equation
(\ref{b3}).
  To make $\partial f/\partial t=0$  in  equation  (\ref{b5}) the correction $g_{E}({\bf k})$ must be the following
  \begin{equation}
g_{E}({\bf k})=-\frac{-df_{0}}{d\epsilon }eE_xk_{y}F_{z}
  \label{b6}
\end{equation}%
This contribution is not symmetric in the $y$-direction. This means that already
the normal (i.e. usual $\partial \epsilon /\partial {\bf k}$) velocity can contribute to the Hall current in the stationary state:

\begin{eqnarray}
J_{yx}^{normal}&=&e\int \frac{d^{2}{\bf k}}{(2\pi )^{2}}g_E({\bf k})(v_y^{(normal)})\nonumber\\
&=&-\frac{e^2E_x F_z}{ (4\pi )}k_{F}^2
\label{jnos}
\end{eqnarray}
which has the opposite sign and is exactly the same in the absolute
magnitude as the anomalous velocity contribution in  the clean limit given by Eq.(\ref{F1}).

\subsection{The side jump}

The anomalous change of energy after the scattering is not the only
important effect of the anomalous shift (\ref{b1}).
The anomalous shift during the scatterings has generally a
component perpendicular to the direction of the electric field.
\begin{equation}
\Delta y({\bf k}, {\bf k^{\prime }})=F_{z}(k_{x}^{\prime }-k_{x})
\label{shift22}
\end{equation}
It does not contribute to the change of energy during the scattering but it shifts a particle along the $y$-axes. If such shifts do not
compensate each other after many scatterings, they should contribute to the total Hall current. This phenomenon is known in the theory of the
extrinsic Hall effect as the side jump. If scatterings happen with the
rate $\omega ({\bf k,k^{\prime
}})$ in average the particle moving with the momentum
${\bf k}$ also acquires the anomalous drift velocity perpendicular to the electric field
\begin{equation}
\left\langle v_{y}^{(sj)}({\bf k})\right\rangle _{imp}=\sum_{\bf k^{\prime }}\omega
({\bf k}, {\bf k^{\prime }})\Delta y({\bf k},{\bf k^{\prime }}) =-F_z k_{x}/\tau _{||}
 \label{sum}
\end{equation}
where
\begin{equation}
1/\tau _{||}= \sum_{{\bf k^{\prime }}} \omega ({\bf k,k^{\prime }})(1-\cos ({\bf k,k^{\prime}})) %
\label{tau1}
\end{equation}
and "$(sj)$" marks the side jump contribution to the physical quantity.

In the equilibrium the side jump does not lead to the Hall current because the anomalous velocity (\ref{sum}) changes
the sign under the transformation $k_x \rightarrow -k_x$.
and the distribution function in the equilibrium is invariant under this transformation.
However, when  the electric field
is applied the non-equilibrium correction to the distribution function
appears which has no such a symmetry under the momentum reflection.

This correction to the distribution function
can be derived by means of the standard approach to the Boltzmann equation.
 Up to the first order in the electric field the standard Boltzmann equation for one band, ignoring
the asymmetric contribution considered in the previous subsection, is%
\begin{equation}
-eE_x v_{x}^{(normal)}(-\frac{\partial f_{0}}{\partial \epsilon })=-\sum_{\bf k^{\prime
}}\omega ({\bf k,k^{\prime }})(f({\bf k})-f({\bf k^{\prime }}))
\label{be2}
\end{equation}
where $f_0({\bf k})$ is the equilibrium distribution function.
Equation (\ref{be2}) has a solution $f({\bf k})=f_{0}({\bf k}) +g({\bf k})$ where to the first order in the electric field
\begin{equation}
g({\bf k})=eE_x\tau _{||}(-\frac{\partial f_{0}}{\partial \epsilon })v_{x}^{(normal)}
\label{g1}
\end{equation}%
$v_{x}^{(normal)}$ is the normal velocity along the electric field, which in our case is
\begin{equation}
v_{x}^{(normal)}=\frac{\partial \epsilon (k)}{\partial k_{x}}=bk_{x}
\end{equation}
here we assumed that the conducting band has a trivial dispersion $\epsilon ({\bf k})=bk^2/2$ where $b=1/m_e$.
The side-jump contribution of impurities to the anomalous velocity leads to the Hall
current
\begin{eqnarray}
J_{yx}^{(sj) } &=&e\int \left\langle v_{y}^{(sj)}({\bf k})\right \rangle _{imp}g({\bf k })%
\frac{kdkd\phi }{(2\pi )^{2}}
\nonumber\\&=&-\frac{e^2E_xF_z}{(2\pi)^2}
\int_0^{2\pi} d\phi \cos ^{2}(\phi )\int d\epsilon_k k^2\delta (\epsilon_F
-\epsilon _{k}) \nonumber\\
&=&-\frac{e^2E_x F_z}{ (4\pi )}k_{F}^2\label{fin2}
\end{eqnarray}
As in the previous impurity contribution, the Hall current due to the side jump has the opposite sign and the same magnitude as the one in the clean limit.
The side jump current appears because the anomalous velocity is proportional to the acceleration
 of the particle but in the stationary state the average acceleration should be zero
 (up to the terms of  the first order in the electric field), namely, while the external electric field accelerates the wave packet during its motion between
 impurities, the impurity potential generally decelerates it. During such  a deceleration the wave packet has the anomalous velocity with the opposite sign
 and hence the side jump contribution should compensate or at least decrease the pure limit result.
The described picture is of course oversimplified, which will be clear from the discussion of a momentum dependent $F_z$.
In reality, the external electric field equally
accelerates all electrons in the Fermi sea but effective deceleration due to impurity scatterings is, in average, seen only by the electrons near
the Fermi level because there the distribution function acquires a correction required to compensate the acceleration by the external field.
Hence the side jump contribution is the property of the Fermi surface while the clean limit Berry phase contribution appears from all electrons even deep in the Fermi sea.

\subsection{Total current and numerical check}

The total Hall current (not including effects of skew scatterings due to asymmetry of the collision term kernel)
is the sum of the clean limit contribution,
of the side jump and of the normal velocity contributions. For the constant $F_z$ we find
\begin{equation}
J_{yx}^{(total)}= J_{yx}^{(clean)}+J_{yx}^{(sj)}+J_{yx}^{(normal)}=-\frac{e^2E_x F_z}{ (4\pi )}k_{F}^2
\label{cfin}
\end{equation}
As it was predicted in the former literature which focused on models with a constant $F_z$,
 the total current has the same magnitude but with the opposite sign as the one in the
absolutely clean system. Our derivation however is
considerably simpler and is straightforward to generalize to a case with a
more complicated band structure such as Rashba coupled 2DEG.

\begin{figure}
\includegraphics[width=3.2 in]{ahepic1.eps
\centering
\caption{Scattering of a particle on impurity. The impurity is assumed to have the shape of a long stripe with linearly growing potential inside. }
\label{Wall}
\end{figure}
To confirm the analytical result (\ref{cfin}) numerically we simulate the motion of
particles according to equations of motions (\ref{dkx1}) and (\ref{om1}).
Initially all particles were prepared uniformly distributed over the
momentum space having  the absolute value of the momentum less
than a specified Fermi momentum. The action of an impurity was simulated by the potential of a wall of a finite thickness
 with a very fast linearly growing potential inside the wall. The wall is sufficiently long to disregard
  the effects on its edges. This type of impurity does not allow the skew scattering mechanism to appear because for every scattering
   on the wall that
  changes momentum from ${\bf k}$ to ${\bf k^{\prime}}$ there is a process when a particle hits the same wall from another side and scatters from
  ${\bf k^{\prime}}$ into ${\bf k}$. Thus both processes have equal probability and $\omega({\bf k,k^{\prime}})=\omega({\bf k^{\prime},k})$.
 Fig.\ref{Wall} demonstrates a scattering on such an impurity. We would like to point to the analogy of the scattering in Fig.\ref{Wall}
 with Goos-H\"anchen's and with Fedorov's shifts in geometrical optics \cite{optics}.

One can consider the effect of the wall on a wave packet as the one
 due to an electric field $E_{\perp}$ acting on it only inside the wall in the direction perpendicular to the wall.
Although the potential in the wall can be strong in comparison with the external electric field, we suppose that the motion inside the wall is still
governed by
the equations of the wave packet dynamics. Such a scattering problem can be solved exactly. This solution shows that for the given type of
 scatterings
the theory of the anomalous shift is valid even if we do not assume that the anomalous velocity term in wave packet equations is small.
This is useful because the bigger anomalous velocity is needed to accelerate the numerical calculations.

 Let components of the momentum of the particle incident on the wall be
$k_{||}$ and $k_{\perp}$ parallel and perpendicular to the wall respectively.
In the presence of an additional external electric field
the total force has generally also a nonzero component parallel to the wall $eE_{||}$ where $E_{||}$ is the
projection of the external electric field on the direction along the wall. Expressions for the final momentum and
 coordinates right after the scattering
are strongly simplified in the limit of large $E_{\perp}$, so that all terms $O(1/E_{\perp})$ can
be dropped. In this limit
 the scattering time is vanishing and in (\ref{om1}) one can disregard the first term in comparison with the second one since
 $\dot{k}_{\perp} \sim E_{\perp}$ is large. Dropping the term with $\partial \epsilon/\partial k_{\perp}$ the equation (\ref{om1}) can be
readily integrated over the time of the scattering leading to the relations $\Delta r_{||}=eF_z(k_{\perp}-k_{\perp}^{\prime})$ and $k_{||}^{\prime}=k_{||}$.
Solving them together with the energy conservation equation $\epsilon ({\bf k})+eE_{||}r_{||}=\epsilon ({\bf k^{\prime}})$
we arrive at following expressions for the momentum of the outgoing particle
\begin{equation}
\begin{array}{l}
k_{||}^{\prime}=k_{||}\\
k_{\perp}^{\prime}=-k_{\perp}-E_{||}F_z
\end{array}
\label{kkk1}
\end{equation}
 In addition, the scattered particle appears
in a point of the interface shifted in comparison to the incident point by the amount.
\begin{equation}
\Delta r_{||}=2k_{\perp}F_z+E_{||}F_z^2
\label{kkk2}
\end{equation}
The shift $r_{||}$ is exactly the anomalous shift in the impurity potential. Note also that, as it follows from
(\ref{kkk1}), when a scattering happens in the additional external
electric field with nonzero projection to the direction of this shift $E_{||}$, the absolute magnitude of the momentum changes, which leads to
the instability of the equilibrium distribution function, discussed in previous sections.
The scattering time in this
limit is small enough to be disregarded so numerically such a scattering can be easily simulated by
choosing the coordinate system related to the wall orientation and updating the momentums and coordinates according to
$(k_{||},k_{\perp}, r_{||}, r_{\perp}) \rightarrow (k_{||}^{\prime}, k_{\perp}^{\prime}, r_{||}+\Delta r_{||},r_{\perp})$,  $r_{\perp}$ is
the same for the incident and the out going particle. In between scatterings equations of free motion in the external electric field are also trivially
solvable. In our simulations we assumed the "noncrossing approximation", namely we suppose
that every scattering happens on a different impurity.
The algorithm consists of two parts. First we generate randomly the distance $L$ to the next impurity.
We suppose that between impurities particles move only under the action of the electric field. The integration of wave packet equations
 leads to the following
trajectories
\begin{equation}
\begin{array}{l}
k_x^{\prime}=k_x+E_xt\\
k_y^{\prime}=k_y\\
x^{\prime}=x+k_xt+\frac{E_xt^2}{2}\\
y^{\prime}=y+(k_y+F_zE_x)t
\end{array}
\label{traj}
\end{equation}
The time $t$ of the motion to the next impurity was estimated from the equation $((x^{\prime}-x)^2+(y^{\prime}-y)^2))^{1/2}=L$.
Solving this relation with the solution (\ref{traj}) we find the
momentum and coordinates of the particle before
the new scattering. In the second step we randomly generate the orientation angle of the impurity, switch into the related coordinate system
 and update  particle's coordinates and the momentum according to
(\ref{kkk1}) and (\ref{kkk2}). Then we return to the initial coordinate system and repeat the circle.
 We repeat this circle sufficiently many times to allow the distribution to relax to the
stationary one (usually a few scatterings is enough),
however the total evolution time was small enough in order to avoid strong heating of the system. In our simulations,
every particle makes about $10^2-10^3$ scatterings during the whole time. To prevent strong heating the electric field is chosen sufficiently
small $E_xl/E_F \sim 10^{-4}$ where $l$ is the typical scattering length and $E_F$ is the Fermi energy.
The total current can be derived as the sum of total displacements of all particles divided by the evolution time.

\begin{figure}
\includegraphics[width=3.2 in]{AHE_fig2.eps
\centering
\caption{Hall conductivity vs strength of the Berry curvature in the model with momentum independent $F_z$. Solid line is the theoretical prediction that includes impurity
scatterings and dotted line is the prediction of the clean limit contribution. Triangles show results of the numerical simulations.
Simulations were performed in units $e=\hbar = m=1$ and  $k_F=1$.}
\label{fig1}
\end{figure}
In Fig.\ref{fig1} we compare the analytical result (\ref{cfin})
with our numerical simulations for the fixed Fermi energy but different
strengths of the spin orbit coupling, and hence $F_z$. Both analytical and numerical
results are in excellent agreement with each other.
This result survives at an arbitrary magnitude of the Berry curvature.

\begin{figure}[h]
\includegraphics[width=2.4 in]{dist1.eps
\centering
\caption{Distribution of particles over the momentum space in the stationary state with electric field applied along the $y-$axes at zero Berry
curvature. Parameters are as follows. $k_F=1$, $E_y=0.003$, $E_x=0$, $F_z=0$. Average distance between impurities is $l \sim 0.5$ in units
$m=\hbar=e=1$.}
\label{dist1}
\end{figure}
\begin{figure}[h]
\includegraphics[width=2.4 in]{dist2.eps
\centering
\caption{Distribution of particles over the momentum space in the stationary state with electric field applied along the $y-$axes at
the non-zero Berry
curvature. Parameters are as follows. $k_F=1$, $E_y=0.003$, $E_x=0$, $F_z=-1$. Average distance between impurities is $l \sim 0.5$.}
\label{dist2}
\end{figure}

In Fig.\ref{dist1} and Fig.\ref{dist2} we visualized the stationary distribution function of particles in the momentum space, calculated numerically
for the system placed in  the uniform electric field.  Brighter areas represent
higher densities. To increase the contrast, we subtracted the initial equilibrium distribution (i.e. without electric field)
 from the calculated one.  In
 Fig.\ref{dist1} the Berry curvature is set to zero. In this case the correction to the equilibrium distribution is symmetric along the
 electric field. Fig.\ref{dist2} shows that when the Berry curvature becomes nonzero, the distribution function
 acquires the additional asymmetric contribution, which obviously deposits to the Hall current.

\subsection{Analogy between extrinsic and intrinsic AHE}
As we showed above, in the AHE induced by Berry curvature there is a possibility of disorder
effects similar to previously studied  extrinsic contributions to Hall current due to gradient terms of
the disorder potential.
In this subsection we discuss how this relation is encoded in the wave packet equations (\ref{dkx1}), (\ref{om1}). We consider here only the case
of a constant Berry
curvature. The wave packet dynamic equations do not arise from a particular Hamiltonian in a sense that coordinates and momentums of a wave packet
are not canonical variables.
Nevertheless, it is possible to make them arise from a Hamiltonian by adding terms of
higher order in the potential gradient. We remind the reader  that equations (\ref{dkx1}) and (\ref{om1})
were derived in the approximation of a smooth potential so that
its higher gradients could be discarded.
Therefore such a procedure should not change the physics at least to the order of the approximation of the
whole theory. Consider the following system
\begin{equation}
\frac{d}{dt} {\bf k}=e {\bf E} - {\bf \nabla}V({\bf r}) -  {\bf \nabla} ({\bf k}\times {\bf \nabla}V({\bf r})) \bf{F} \label{dkx11}
\end{equation}%
\begin{equation}
\frac{d}{dt} {\bf r}=\frac{\partial \epsilon ({\bf k})}{\partial {\bf k}} - (e {\bf E} - {\bf \nabla}V({\bf r}))\times {\bf F}
\label{om11}
\end{equation}
Except for one term of the second order in gradients of the potential the system is equivalent to the wave packet equations
(\ref{dkx1}),  (\ref{om1}).
The new system (\ref{dkx11}), (\ref{om11}) already corresponds to the classical Hamiltonian evolution with the following Hamiltonian

\begin{equation}
H({\bf k, r})=\epsilon({\bf k}) - {\bf F} ({\bf k}\times (e{\bf E}-{\bf \nabla} V({\bf r}))+V({\bf r})-e{\bf E}{\bf r}
\label{hhhhh}
\end{equation}
This Hamiltonian has the same structure as in typical models of the extrinsic AHE \cite{{Berger1},{Berger2},{Berger3}} and the Berry
curvature now plays the role of an effective spin orbit coupling constant. As we mentioned,  the
main contributions to the extrinsic Hall current  have been proved to be the side jump and the skew scattering.
In our previous calculations, including numerics, we ignored the
skew scattering mechanism,
nevertheless  the skew scattering  can be calculated by same
weave packet techniques because the second term in the rhs. of (\ref{hhhhh})  is responsible
for both skew scattering and the side jump contributions in the extrinsic AHE.
Note also that the skew scattering current will depend on the Berry
curvature and thus will also have a geometric interpretation. The fact that the side jump is the only
other surviving contribution in the extrinsic AHE is in agreement with our previous
findings.

\section{Rashba 2DEG with exchange coupling}

Recently studied systems with AHE such as DMS and Rashba 2DEG have Berry curvature that strongly
depends on momentum of the wave packet \cite{Dimi}. When $F_z$ is no longer a constant the simple arguments leading to canceling of some terms
may not work. One
can notice that when an electron decelerates it has in general different momentum
than when it accelerates,  in other words the uniform electric field
accelerates all electrons down to the bottom of the Fermi sea but impurities
produce nonzero deceleration in average only for electrons near the Fermi
surface. The Berry phase acquired by accelerating
electrons depends now not only on the acceleration but on the momentum itself
therefore contributions from impurities and from uniform electric field not
necessarily cancel each other.

The Hamiltonian of R2DEG with the electric field along the $x$-direction and
the exchange field in the $z$-direction is

\begin{equation}
H=H_{0}+H_{SO}+H_{exch}-eE_{x}x+V_{imp}  \label{hs0}
\end{equation}
\begin{equation}
H_{0}=\frac{bk^{2}}{2}\sigma _{0},\,\,\, b=1/m  \label{h0}
\end{equation}
\begin{equation}
H_{SO}=\lambda (k_{y}\sigma _{x}-k_{x}\sigma _{y})  \label{hso1}
\end{equation}
\begin{equation}
H_{exch}=h\sigma _{z}  \label{exch1}
\end{equation}
where $V_{imp}$ is the impurity potential.

Diagonalizing the unperturbed part of the Hamiltonian we find the energy dispersion

\begin{equation}
\epsilon_{\pm} (k) = bk^2 \pm \sqrt{(\lambda k)^2+h^2}
\label{disp}
\end{equation}
There are two bands, the minor band has the plus sign in the above expression. Fermi momentums can be derived by inversion of the equations
(\ref{disp}). We denote them as $k_{F-}$ and $k_{F+}$ respectively for the major and minor bands.
The Berry curvature is different for different bands
\begin{equation}
F_{z}^{s}=2Im\left\langle \frac{\partial u^{s}}{\partial k_{y}}|\frac{%
\partial u^{s}}{\partial k_{x}}\right\rangle  \label{adi2}
\end{equation}%
here $\left\vert u^{s}\right\rangle$ is the Bloch state in the absence of
electric field and impurities and $s=\pm$ is the index of the band: the plus is for the minor and the minus is for the major one.
In the case of the Hamiltonian (\ref{hs0}) the Berry curvature is \cite{Dimi}, (see also Appendix for an alternative derivation).
\begin{equation}
F_z^{s}(k)=-s\frac{h \lambda^2}{2[(\lambda k)^{2}+h^2 ]^{3/2}}
\label{bc1}
\end{equation}
at  $\lambda k<<h$ this gives $F_z^{s}(k)\approx -s \lambda^2/(2h^2)=const$ and we reduce the problem to the one considered in previous sections.
In the opposite limit at $\lambda k>>h$ we find
\begin{equation}
F_z^{s}(k)\approx -\frac{sh}{2\lambda k^{3}}
\end{equation}

The anomalous velocity has the same magnitude but different signs for different bands so filled states
with the same $\mathbf{k}$ from different bands will compensate each other in calculations of the clean contribution and
to find the Hall current we should only integrate over uncompensated states of the  major band. The Hall
current from the unperturbed electron distribution function in the clean case  is
\begin{eqnarray}
&&j_{yx}^{(clean)}=e\int\limits_{0}^{2\pi }d\phi \int\limits_{k_{F+}}^{k_{F-}}\frac{kdk}{(2\pi )^{2}}
(eE_xF_z^{-}(k))\nonumber\\&=&e\int\limits_{0}^{2\pi }d\phi
\int\limits_{k_{F+}}^{k_{F-}}\frac{kdk}{(2\pi )^{2}}\frac{eE_xh \lambda ^2}{2[(\lambda k)^{2}+h^2]^{3/2}%
}\nonumber\\
&=&\frac{e^2E_x}{2(2 \pi)} \left( \frac{1}{\sqrt{1+(k_{F+} \lambda /h)^2}}\right.\nonumber\\&&\left.
-\frac{1}{\sqrt{1+(k_{F-} \lambda /h)^2}} \right)
\label{fin1}
\end{eqnarray}
in the case $E_{F}>>  \lambda k_{F\pm}>>h$ the expression (\ref{fin1}) is simplified
\begin{eqnarray}
j_{yx}^{(clean)}&\approx&
\left\{ \lambda k\ll E_{F}\approx \frac{k_{F}^{2}}{2m}\right\} =\frac{%
e^{2}E_xh(k_{F-}-k_{F+})}{(2\pi )2\lambda k^{2}}\nonumber\\&=&\left\{
(k_{F-}-k_{F+}) \approx 2\lambda m\right\} =\frac{e^{2}E_xh}{4\pi E_{F}}
\label{fin11}
\end{eqnarray}%
note that here $k_{F+}$ is the Fermi momentum of the minor band.
The above formulas are valid when there are electrons in both bands. At a sufficiently low Fermi level $(E_F<h,\lambda k_{F-})$ the minor band becomes
depleted and the transport is only in the major band. In this case the clean limit Hall current is
\begin{equation}
j_{yx}^{(clean)}
=\frac{e^2E_x}{2 (2 \pi)} \left(1 - \frac{1}{\sqrt{1+(k_{F-} \lambda /h)^2}} \right)
\label{fin2}
\end{equation}
We address next the effects of impurity scattering within the formalism that we have developed.

As in the case of the constant Berry curvature, the
 non-equilibrium contribution to the distribution function is the sum of the usual one $g^s ({\bf k})$,
  which appears to compensate the electron acceleration
\begin{equation}
g^s ({\bf k})=eE_x\tau _{||}(-\frac{\partial f_{0}}{\partial \epsilon })v_{s,x}^{(normal)}
\label{g11}
\end{equation}%
 and of the anomalous one $g_{E}^s({\bf k})$
   due to the shift of the kinetic energy of the scattered particle. We suppose here
   that the impurity potential is weak, namely $V({\bf r})<<E_F, \lambda k_F$ and disregard the variation
of the Berry curvature near a wave packet during a scattering because the absolute magnitude of the momentum does not change appreciably.
The derivation of the anomalous correction is analogous to (\ref{b3})-(\ref{b6}).
  \begin{equation}
g_{E}^s({\bf k})=-\frac{-df_{0}}{d\epsilon }eE_xk_{y}F_{z}^s
  \label{bb6}
\end{equation}%
The normal velocity of the wave packet is
\begin{equation}
v_{s,x}^{(normal)}=\frac{\partial \epsilon_s (k)}{\partial k_{x}}  \label{vnx}
\end{equation}

The expression for the drift velocity due to the side jumps along the $y$-axes is the same as in (\ref{sum}).
The side jump current is
\begin{eqnarray}
&&j_{yx}^{(sj) }=\sum_{s=\pm}e\int \langle v_{s,y}^{(sj)} (\mathbf{k}) \rangle _{dis} g^s(\mathbf{k)%
}\frac{kdkd\phi }{(2\pi )^{2}}\nonumber\\&=&\sum_{s=\pm}
\int d\phi \frac{\cos ^{2}(\varphi )}{(2\pi )^{2}}\int d\epsilon_{s,k}  e^2 E_xF_z^s (k)k^2 \delta (E_F
-\epsilon _{s,k})= \label{fin22} \nonumber\\
&=&\frac{he^{2}E_x \lambda^2}{2 (4\pi )}\left(\frac{k_{F+}^2}{[(\lambda k_{F+})^{2}+h^2]^{3/2}}\right.
\nonumber\\&&\left.
-\frac{k_{F-}^2}{[(\lambda k_{F-})^{2}+h^2]^{3/2}}
\right)
\end{eqnarray}
At $E_F>>\lambda k_F>>h$ this expression can be simplified
\begin{equation}
j_{yx}^{(sj) } \approx \frac{he^{2}E_x}{8\pi E_F}
\label{alsdfj}
\end{equation}
If $E_F<h$ only the major band survives and
\begin{equation}
j_{yx}^{(sj) } = \frac{-he^{2}E_x \lambda^2}{2 (4\pi )} \frac{k_{F-}^2}{[(\lambda k_{F-})^{2}+h^2]^{3/2}}
\label{fin222}
\end{equation}

The normal current contribution is
\begin{equation}
\begin{array}{l}
j_{yx}^{(normal)}=\sum_{s=\pm}e\int \frac{d^{2}{\bf k}}{(2\pi )^{2}}%
v_{s,y}^{(normal)}g_{E}^s({\bf k})= \\
\\
=\sum_{s=\pm}
\int d\phi \frac{\sin ^{2}(\varphi )}{(2\pi )^{2}}\int d\epsilon_{s,k}  e^2 E_x F_z^s (k)k^2 \delta (E_F
-\epsilon _{s,k})
\end{array}
\label{bb7}
\end{equation}%
Comparing the last expression with the one for the side jump current (\ref{fin22}) we find that they are different only by an exchange of
$\cos(\varphi)$ and $\sin(\varphi)$ under the integral over the angle. Thus we arrive at the general result
\begin{equation}
j_{yx}^{(normal)}=j_{yx}^{(sj) }
\label{jisj}
\end{equation}
Finally,
\begin{equation}
j_{yx}^{(total)}=j_{yx}^{(clean)}+j_{yx}^{(sj) }+j_{yx}^{(normal)}
\label{totl}
\end{equation}

As it is seen from (\ref{alsdfj}), (\ref{fin11}) the side jump contribution may not change the sign in comparison with the
clean contribution for sufficiently large
Fermi energy. This is very distinct
from the case of the constant Berry curvature where such a
contribution exactly cancels the pure one. At the limit $E_F>>\lambda k_F>>h$ we find for the total current
\begin{equation}
j_{yx}^{(total)}\approx \frac{he^{2}E_x}{2\pi E_F}
\label{totlim1}
\end{equation}
The total Hall current not only has the same sign, as the clean limit prediction, but also increases due to scatterings. Note also, that
up to a coefficient of the order unity, in this limit, the total current has the same dependence on various parameters.

\begin{figure}
\includegraphics[width=3.0 in]{fig41.eps
\caption{(Color online) Hall conductivity vs the Fermi energy in the R2DEG. Black line is the pure limit Berry phase prediction. The red curve shows the prediction
of the theory that includes impurity
scatterings (\ref{fin22}), (\ref{jisj}).
Data are given in units $e=\hbar = m=1$ for the case $h=0.7$, $\lambda = 0.4$. Sharp change in the behavior above $E_F=0.7$ is due to the
appearance of electrons in the minor band. }
\label{Rcomp}
\end{figure}

In Fig.\ref{Rcomp} we compare the theoretical prediction of Eqs. (\ref{totl}) with the prediction of the pure Berry phase contribution (\ref{fin1}).

\section{Discussion and Conclusion}

We calculated the anomalous Hall current in the presence of a smooth disorder potential by
combining the wave packet dynamic equations with  the classical Boltzmann equation.
 For the case of a constant
Berry curvature our results are in agreement with some known predictions of the very earliest works on AHE. The gauge invariance of our approach
clarifies the physical meaning of various disorder
contributions to the Hall current and reveales the relation between
the extrinsic, related to the gradients of the disorder potential,
 and Berry curvature effects in the presence of disorder.

We have shown that early results, like that of the Luttinger's sign reversal prediction,
 cannot be used directly for new applications such as diluted magnetic semiconductors, where the
Berry curvature is strongly momentum dependent.

Our prediction for the Hall current Fig.\ref{Rcomp} is distinct from the clean limit (or the pure Berry phase) one. Thus the total Hall current changes the sign when the Fermi level increases.
In contrast, the clean limit prediction
for the models considered remains of the same sign.
The filled states in both bands
with the same momentum compensate each other,
hence for the clean case the band having more filled states always wins. In contrast,
impurity contributions are sensitive not only to the
density of states near the Fermi level, but also to the
magnitude of the Berry curvature near the Fermi level.

The change of sign of the Hall current as a function of chemical potential originates from the competition between two bands.
The minor band has the smaller number of filled states than the major one but it also has lower $k_F$ and hence the stronger $F_z(k_F)$.
According to our calculations,
such a change of sign should generally happen when the
chemical potential is close to the depletion point of the minor band.
When the minor band is totally
depleted we always observe the reversal of the sign of the Hall current in comparison to the clean limit contribution.
We also note that such a competition should be applicable to the skew scattering mechanism as well. This follows from the fact that the
strength of the skew scattering should be proportional to
the Berry curvature at the Fermi surface.

Our results can be generalized to DMS and although in this case the complicated
behaviour of the bands, as compared to the R2DEG, may change the quantitative behavior
there is still a competition in DMS
of Hall currents from major and minor bands and Berry curvature is also usually decreasing
when momentum is increasing. However the intricate dependence of the clean limit AHE observed
in these systems versus the simple dependence observed in the R2DEG will require a careful analysis.

Although we have verified most our predictions by numerical simulations,
the correspondence between the wave packet approach and the evolution of a
true quantum system with disorder remains to be investigated.
An effect not taken in to account in our calculations is
 that the spin density in the wave packet polarizes when the wave packet
is accelerated \cite{Dimi2}. This effect is crucial for
the Spin Hall Effect and its importance for calculations by the Boltzmann equation
should be understood.

The final theory of disorder in the AHE can be achieved
only by purely quantum mechanical calculations for example, based on the  Keldysh technique.
At present new approaches to systems with Berry curvature have
emerged \cite{Haldane}, as well as new mechanisms to generate the anomalous Hall current
\cite{Bruno-rods}, but we
believe that the wave packet approach combined with the classical
Boltzmann equation is worth studying because it provides the simplest,
to our knowledge, demonstration of the related physics and the wave packet equations
themselves have been well justified by the quantum theory.

\noindent
 {\it Note added}. After completion of this work we became aware of
the related effort by V. K. Dugaev {\it et al.} \cite{Dugaev} of a more quantum mechanical approach
to the problem with similar qualitative conclusions. Our approach
however is quite different and in combination with this work may shed further light on the
physical interpretation of the effect.

\noindent
 {\it Acknowledgments}. The authors are greatful for insightful and useful discussions with
A. H. MacDonald and V. L. Pokrovsky. This work was supported by Welch Foundation, by DOE
grant DE-FG03-02ER45958 and by NSF under the grant DMR-0115947.

redpajama_set_name: RedPajamaArXiv


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1. How can I purchase CX Design lighting?
Any item from the CX Design lighting collection can either be purchased online at cxny.com, or by calling us in New York at 212.431.4242 or toll free at 888.431.4242. Many of the items in our collection are exclusive to CX Design and must purchased through us directly. Select items can also be purchased from any of our qualified dealers. One of the advantages to working with one of our reputable retailers is the opportunity to see a wide range of CX Design lighting products in person and enables you to work with a well trained and experienced sales associate.
2. Can I call CX Design to help me with order process?
Absolutely. In fact we encourage you to call us with any questions or assistance you may require to find the right lighting solution for your needs. We are happy to provide you with our expertise. You may contact us anytime at info@cxny.com or call us in New York at 212.431.4242 or TOLL FREE at 888.431.4242, 9:00 - 6:00 EST Monday thru Friday.
Yes. Visiting our showroom is an excellent way to view our collection and receive the most personalized service. Our showroom is located in Soho at 304 Hudson Street 3rd Floor, New York, NY 10013. Click here to make an appointment, or call us in New York at 212.431.4242 or TOLL FREE at 888.431.4242.
4. Are there ordering guidelines you recommend?
Yes. Two of the most important consideration to factor in the decision is the application of the fixture. Residential interiors pose different requirements to those found in commercial settings. It is important to consider the appropriateness of scale and color when choosing for these settings. Our single diffusers range in scale from 5 inches to 25 inches. The smaller the diffuser the more versatile the application. The mini or smaller scaled diffusers may be used individually in a small space as single pendants or clustered on a chandelier body. The larger scaled diffusers often work well as stand alone pieces and create a more dynamic and central statement. Color is very important to consider. Although all of the Scavo colors are very warm and easy to incorporate into a range of settings, we feel that the more subdued tones are more versatile and are more appropriate for residential interiors.
5. Do you have glass color samples?
Yes. Please call in New York at 212.431.4242, TOLL FREE at 888.431.4242, email at info@cxny.com or fax 212.431.4286 your request for the specific color sample(s) that you would like to receive.
All orders shipped to addresses within New York state will be charged 8.875% of the total order.
8. Is my online order secure?
We are committed to protecting your privacy and providing a secure and safe shopping experience. When you place orders or access your account, all information is encrypted during transmission using SSL (Secure Sockets Layer) technology. We do not sell, trade, or disclose your personal information to others. Your information is collected solely to process and fulfill your order.
9. How and where do you ship?
All orders are shipped UPS ground unless otherwise specified. We do not ship to PO Boxes due to UPS restrictions. Our shipping and handling rate is 6% of the total order for orders being shipped within the 48 contiguous states and 8% for orders shipped to Alaska, Hawaii, Puerto Rico, and Canada. For orders being shipped to Canada, our shipping fee does not include additional taxes, duties and brokerage fees. These charges are billed and collected by UPS upon receipt. Please contact us at info@cxny.com or call us in New York at 212.431.4242 or TOLL FREE at 888.431.4242 for international shipping rates, or if you require expedited shipping.
10. What if something is missing or arrives damaged?
Our products are packed to exceed UPS requirements and are shipped free from defects. If a damage has occurred in transit, please notify us within 7 days to arrange for a replacement or to ensure that we can file a claim with UPS. All other claims such as incorrect item, shortage, and quality of goods must be made to CX Design within seven days of receipt.
11. What is CX Design's production lead-time?
We make every effort to stock as many styles and colors and typically ship in stock orders within two weeks. All orders are subject to availability. If you would like to know if an item is in stock prior to placing order please contact us at info@cxny.com or call us in New York at 212.431.4242 or TOLL FREE at 888.431.4242. Otherwise we will automatically notify you with the estimated delivery date after we have received your order.
12. Do you work directly with the trade? Do you offer volume discounts?
Yes. Please contact us at info@cxny.com or call us in New York at 212.431.4242 or TOLL FREE at 888.431.4242.
Due to the hand crafted nature of our work, we do not accept returns. We will replace anything that was damaged in transit or if an incorrect item was received. We are happy to make an exchange and work with you to ensure that you are satisfied with your CX Design purchase. All exchange transactions must take place within 30 days of invoice date and items must be returned in resalable condition. If there are circumstances that require us to accept a return please note that this will be subject to a 25% restocking fee and the item must be in resalable condition. A credit will be issued towards a future purchase but we cannot offer any refunds.
14. How do I contact CX Design?


Dilley ISD does not discriminate against any employee or applicant for employment because of race, color, religion, gender, national origin, age, disability, military status, genetic information, or on any other basis prohibited by law. Additionally, the district does not discriminate against an employee or applicant who acts to oppose such discrimination or participates in the investigation of a complaint related to a discriminatory employment practice. Employment decisions will be made on the basis of each applicant's job qualifications, experience, and abilities.
The Human Resource Department is responsible for providing a comprehensive program of benefits for its employees as well as a competitive compensation package designed to attract and retain qualified staff. The Human Resource Department also hires and trains substitute teachers and paraprofessionals for filling employee absences.


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Love And Freedom In Celaena's Warmth Behind The Mask
INTRODUCTION " We all bear scars… mine just happen to be more visible than most." Imagine at 18 years old you were imprisoned in a death and torture camp, would you survive? Celaena was just skin and bones when the captain of the guard offered her freedom. Celaena knew it was freedom or death but she had to pay a price, she would kill for the king, be the kings champion. As she stayed in the castle she found love, friendship, and an evil so terrible it filled the castle with demons and death. This companion book is about how love and freedom was a motivation that drove Celaena to fight till her death. Also about the difference between the way someone portrays themself to be than the way they actually are. It's about other central themes…show more content…
As Celaena started to become familiar with him she noticed he had empathy and unlike his father he had a humane nature that Celaena loved. For example, after Dorian's father ordered his soldiers to kill 500 Eyllwe rebels he said " I heard about those butchered rebels, and I- I'm ashamed… He swallowed, his eyes stinging. 'You won't believe me. But… I don't want to be apart of that. I can't call myself a man when I allow my father to encourage such unforgivable atrocities.'"(Maas,2012,pg.260) This conveys the theme because he is known to be brutal but in fact he is the complete opposite. He is compassionate and cares for…show more content…
They'd stop their laughing if they knew her true name, if they knew that this 'jewel thief' could skin them alive without a knife" (Maas, 2012, Pg.88) She generally shows disgust towards who look down on women as tools instead of equals. They judged her because of her gender not because of her ability or skill. This is an important chapter because gender inequality is still a big issue in society. Females are generally thought to be weaker and less intelligent than males. However in this book, the female main character is courageous, intelligent and stronger than most men in Adarlan. This is important because this shows young adults to live up to their greatest potential even if people don't believe in them. Especially young woman who aspire to do jobs society portrays as "men's jobs." Women can do anything they put their minds
In Fyodor Dostoyevsky's 'Crime And Punishment'
Through his inability to suppress his erratic behavior and overcome his overwhelming sense of guilt, he proves that he is just like the rest of humanity. He denies the idea that he not superior. He continues to justify the murders in effort to prevent him from losing his conception of himself as a
Pride In Romeo And Juliet
Tybalt does not see things peaceful like Benvolio. He prefers violence over peace and pretends to be judge, jury, and executioner for the Capulets. Tybalt's pride in his name causes much violence and the deaths of many characters. The houses' pride in their names affects everyone around them but they are too caught up in their own feud to care. An example of the effect the feud has on others is Mercutio.
A Thousand Splendid Suns Character Analysis
Mariam also suffered the torments imposed on her by the men in her life, sharing a similar fate as her mother, Nana, in a way. Nevertheless, Mariam is not a fallen warrior but a victor. Contrasting from Nana, Mariam fought her battle with resistance rather than endurance. She broke free of the oppressive culture and realized her self-worth in the end. Fariba is one of first non-submissive females of the novel and was portrayed as the woman with a progressive mindset.
Dr Jekyll And Mr Hyde Case Study
There is something wrong with his appearance; something displeasing, something down-right detestable. I never saw a man I so disliked, and yet I scarce know why." (Stevenson 5). It is no accident that Enfield depicted Hyde as a being of displeasing and repulsive appearance. Hyde is a manifestation of everything vicious and evil in human nature, so such well-mannered and benign person as Enfield could not like it. It is an important moment that describes how people see the evil in its pure form.
Morals In Ender's Game
That guilt he felt at the end, the actions he took during, and the prevention he tried before all are the signature marks of a good person put under unbearable stress and in situations that no 10 year old should have to deal with. John Kessel said "Ender is at heart a pacifist. When Dink justifies Ender's beating up Bonzo (Bonzo meant to kill Ender, Bonzo was a troublemaker, he had superior strength and size), Ender breaks down and cries. "I didn't want to hurt him!" he insists. "Why didn't he just leave me alone!"(p. 233) (p7) Nothing could be closer to the
The Struggle In Edgar Allen Poe's 'Cask Of Amontillado'
Nevertheless, Montresor gets ultimate revenge since he murdered Fortunato making the reader's feel shocked. The compassion readers feel is for Fortunato for the reason that he should not have got that brutal way to die. Instead, Montresor should have just confronted him and worked things out. Montresor explains, "But the very definitiveness with which it was resolved precluded the idea of risk" (1). Before Montresor said this, he explained how he will not tolerate with a bully.
Flipped By Wendelin Van Draanen And Crash Short Story Analysis
Even though they are supporting a different cause. Both characters stand up for what is the right thing. In Crash the Main character Abby is really strong in her belief even though she is just doing it for being famous, she is just protesting to be famous. They both are protesting for a stop to destruction against nature. She stands up against her mom for protesting, which basically means that she is stubborn in her beliefs.
Ideas In Oedipus And Antigone
Even though, one of the biggest changes is that the tyrant Creón now is a dictator even more perverse and cruel than in "Antigone". Moreover, in the act of love and loyalty to her friends Antígona is considers a traitor to the city and the punishment for this is death unless she confesses to her crimes. Previously, Antígona challenges the government and Creón himself when she buries the two brothers Tavares in their own land. They were supposed to be exposed to the public eye as a warning for everyone who dare to defy Creón's dictatorship. One of the best traits of Antígona is her stubbornness and strength of her heart to not let anyone manipulate her in her way to the true goal which is to see justice.
Losing A Grip On Life In Tim O Brien's The Things They Carried
He hated himself. He had loved Martha more than his men, and as consequence Lavender was now dead." (Tim O'Brien 346) Lt. Jimmy Cross knew that with this burden he could never forgive himself. Lt. Jimmy Cross wasn't the only one who carried guilt, but all the soldiers in general."They carried the soldier's greatest fear, which was the fear of blushing. Men killed, and died, because they were embarrassed not to." (Tim O'Brien 349) and the things "They carried all they could bear, and then some, including a silent awe for the terrible power of the things they carried." (Tim O'Brien 341) They knew that the weapons they were carrying was the main cause of mass destruction and the power was through the tip of their
Self-Identity And Self Identity In The 20th Century
Instead of being kind and doing whatever it takes to keep men happy, she is described as "the devil" and having "evil in every pocket (192)." The reason for it is because she does not act like a woman from her era, she is difficult and, in some cases, unpleasant to be around, traits not usually associated with women of the 1950s. Within the novel she steals thirty thousand dollars, manipulates and even kills. She is depicted as being "death herself (252)" because of how easily she breaks out of the mold that is pictured when thinking of women in the 1950s. Despite how much she seems to cross that line, she is also very feminine and alluring. Easy describes her flaws, such as eyes that are too close together as endearing and adding to her façade of a vulnerable damsel in distress.
More about Love And Freedom In Celaena's Warmth Behind The Mask
Capital punishment in the United States


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DU Admissions: Technical Glitches Hinder Online Registration Process
The DU commenced its online registration process at 8 pm on Thursday and said within 24 hours, 1,01,811 students had registered on the portal.
Education | Press Trust of India | Updated: June 01, 2019 11:47 IST
DU Admissions: Students Face Technical Glitches During Online Registration Process
Delay in receiving OTP and non-functioning online calculator were the issues students faced when they tried to register on the Delhi University's online portal, which went live on Thursday. The DU commenced its online registration process at 8 pm on Thursday and said within 24 hours, 1,01,811 students had registered on the portal.
However, on the first open day at the Delhi University, several students and their parents complained that the online calculator, which is a new feature introduced on the portal this year, was not functioning properly.
"After logging in and keying in my child's marks, I chose the suggestive online calculator to calculate the best of four aggregate, but it picked up random marks and gave a wrong percentage," said a parent.
An admission official said the online calculator is not yet functional and will only be made functional when the cut-offs are announced. However, varsity officials had initially admitted that there was a problem with the online calculator.
Another parent, alleged these were delaying tactics by the DU and by the time the cut-offs will be announced, the varsity would have rectified it. The parent also said the varsity should have announced it earlier that the online calculator will only be required when the cut-offs are announced.
Another problem that arose was the delay in getting one time password (OTP) required to complete the admission process. "I had registered on the DU portal on Thursday night but did not get the OTP during the 15 minute mandatory time. Now, I am worried whether I will be able to register again on the website with the same email ID I used or not," said S K Vijay, a parent, from Saket.
Another parent said, "I had registered on the Delhi University admission portal at 9.30 pm on Thursday and after filling in the details, I was informed that the OTP will be sent to my phone within 15 minutes. I received the OTP at 4.38 am on Friday." Other parents also had similar complaints and the varsity officials admitted that since there was too much traffic on the admission portal when it went live, there was delay in sending OTPs. They said these issues were not experienced on Friday.
Vinod Tiwari, who had come from Lucknow, said, "My daughter had filled in the marks for all the subjects but after we got a printout, her marks for Biology were missing from the printout. We informed about this to the officials and even wrote an email to DU Registrar about it. They said the marks are there in the database and we should not be worried."
This year, the officials claimed that the portal has been made mobile-friendly and will even function on 2G network. Every year, there used to be reports about server crashing due to high traffic, but officials said this year the admission process till now has been glitch-free.
Over 75 Engineering Colleges To Shut Down: Report
Delhi University Expected To Release Fifth Cut Off List Soon
Delhi University Entrance Test Result, Counselling Schedule Released
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Delhi UniversityDU admission


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Le Moyne Junior Casts an Impassioned Vote for Biden Following the Loss of her Sister to COVID-19
Natalie (left) and Adeline (right). [Photo provided by Natalie Fagan]
Olivia Poust, Editor-in-Chief
Natalie Fagan, 20, is a junior at Le Moyne College studying English with a concentration in literature. She is from Lafayette, NY.
For Natalie Fagan, the choice to vote against Trump was always clear. After COVID-19 took the life of her older sister, however, her vote took on a new meaning.
"As a privileged, white, cis-gender woman, I don't feel particularly under attack by Trump. But I recognize the marginalized groups who are affected by him, which is why I knew I would never vote for him to be elected," said Fagan. "But after my sister passed away, it became very personal to me in a way that it couldn't before. Because as much as I support these other groups, I didn't know what it was like to be hurt by this administration."
Her sister, 28-year-old Adeline Fagan, was an OB/GYN resident physician in Texas and contracted COVID-19 on July 8 while doing a rotation in the ER, where she worked with COVID-19 patients, according to the GoFundMe page run by her family.
After initially being treated with respiratory therapies, Adeline was intubated and placed on a ventilator. Even on the ventilator, she was unstable, so doctors placed her on extracorporeal membrane oxygenation (ECMO). On September 19, 2020 Adeline passed away.
Fagan said she understands that COVID-19 deaths were unavoidable, but she believes that the Trump administration's mishandling of the pandemic response resulted in an excessive and unnecessary loss of lives. Lives like Adeline's.
"I just feel like the irresponsibility on the part of this administration is to blame for the amount of victims we have lost to COVID," said Fagan. She explained that Adeline lived and worked in a state where Trump held mask-less rallies, most likely leading to more cases of COVID and putting frontline workers like Adeline at risk.
In addition to Adeline's work as a doctor, Fagan's other two sisters are in or pursuing careers in the medical field, making healthcare a common topic of discussion for the family.
Universal healthcare is an issue that Fagan has supported long before the pandemic. Looking at it through the lens of COVID-19, Fagan stated that she finds it deeply unjust that some people, especially people of color, are being disproportionately affected by coronavirus because they cannot afford to receive treatment.
"To think that there are people out there that don't have the opportunity to get treated…" said Fagan. "My sister died, but if she had survived, it would have been mostly because of the medical services that she received. Think about all those people who are getting COVID that cannot go to the hospital because they can't afford it. They have no hope. My family clung to hope that my sister was going to get better. Imagine having no hope."
She emphasized her belief that in America, there is a prioritization of money over the well-being and lives of its citizens, which she stated is demonstrated through the healthcare system and further proven at the polls.
"Everybody has a right to vote the way they see fit, but I think you need to look in the mirror at your morals and your values if you think the amount of money you make is more important than the lives that are being lost in this pandemic," she said.
When considering how American voting decisions may have been affected by the pandemic, Fagan referenced conversations in which people have told her their undecided vote was swayed by the way the government handled the pandemic.
"The thing about COVID is that it doesn't discriminate. It doesn't care if you're a Republican; it doesn't care if you're a Democrat," said Fagan. "It's killing people of all ages, of all socio-economic classes, and I think a significant percent of the people that were voting for Trump have now switched because they were affected by COVID and saw how it could have been avoided by strong leadership."
She explained that in his refusal to wear a mask or pass federal mask mandates, Trump set an example that was followed by many of his supporters and politicized a pandemic.
Fagan fears for the future of the country, even without another four years of a Trump administration. "I truly do believe that the wounds Trump has inflicted on this nation will take a long time to heal."
She stated that she hopes Biden can begin to make this change, but acknowledges the vast impact that Trump's presidency has had over the soul of America and how much work is needed to reverse it.
In a video posted to her Instagram, Fagan urged voters to keep Adeline's story in mind as they took to the polls. "When you go to your voting place and you sit down to cast your ballot, if you need one more reason to vote for Biden, please, please look at my Instagram page and look at my sister's beautiful face… Tonight, I voted for Biden for my sister Adeline. Who are you voting for?"
The Election
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Le Moyne joins growing list of colleges to require COVID-19 vaccinations for students
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Christian Carr elected SGA President for 2021-22 academic year
New Mental Health Student Task Force will help carry student concerns to administration
What should Le Moyne expect as SU sees a spike in COVID-19 cases?
Conversations between SGA and administration offer hope and growth
Amidst loss, Le Moyne students voice their concerns for change regarding mental health on campus
'Phins Take a Stand: Student Protesters Demand Change in Mental Health Support On Campus
The student-run news site of Le Moyne College.


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The Riverdale Spin-Off Will Be a Fashion Musical Drama Based on Katy Keene
by Brooke Marine
Photo by @WriterRAS. Archie Comics.
The Riverdale universe is officially expanding with a new character: a fashion girl named Katy Keene.
It would appear that television production magnate Greg Berlanti and Archie Comics maestro Roberto Aguirre-Sacasa are really running things over at The CW—per The Hollywood Reporter, Berlanti's Riverdale spin-off is officially underway, along with a handful of other ordered pilots including the forthcoming Jane the Virgin spin-off, the Nancy Drew reboot, and a serialized version of Lost Boys for the 2019-2020 season. The Riverdale spin-off, based on Katy Keene (a character introduced into the Archie Comics universe in 1945) could be the next iconic Archie character to bolster the success of other series from the publisher, including Riverdale and Chilling Adventures of Sabrina.
So, who is Katy Keene? Well, according to Archie Comics she is "America's Queen of Pin-Ups and Fashions" and of course also happens to be a model, actress, and singer. With a look similar to the iconic Bettie Page, Katy Keene was created by Bill Woggon and gained popularity in the 1940s and 1950s. She was often featured in the actual comic book as a paper doll for readers to cut out, and though her popularity waned after the 1960s, she had a revival in the 1980s.
According to THR, The CW's Katy Keene will be a musical drama following "four aspiring artists trying to make it on Broadway, on the runway and in the recording studio," which sounds like it will be less Jane By Design and more like those later seasons of Glee where everyone moved to New York for show business. It also doesn't seem out of step with the Riverdale television universe, especially since that show has had its fair share of musical episodes and recently announced that there would be at least one more based on Heathers: The Musical. Not only does Katy Keene want to be discovered for her modeling, but she has major Broadway aspirations as well. Katy Keene's superstitious best friend (and fellow model) Lucki Lorelei, her boxer boyfriend K.O. Kelly, and her little sister whose name is literally Sis round out the gang in the Katy Keene universe. The comic book heroine also competes with her opponent Gloria Grandbilt, a rich blonde who continually tries to take Katy Keene's job and her man, which gives the impression that there could be a hint of Gossip Girl-esque rivalry in the works for the series.
Since Katy Keene was only just picked up for a pilot order, casting announcements have yet to be made, but it would make sense for her to star in a crossover episode and make an appearance in the upcoming season of Riverdale after Sabrina Spellman shows up in town.
Related: Sabrina Spellman Is Finally Coming to Riverdale
comics Riverdale television


How much is Herbert Hoover worth? – Wondering how wealthy & rich is Herbert Hoover? Or maybe you're just curious about Herbert Hoover's age, body measurements, height, weight, hair color, eye color, bra & waist size, bio, wiki, wealth and salary?
Herbert Clark Hoover (West Branch, Iowa, August 10, 1874 – New York, October 20, 1964) was the thirty-first President of the United States, taking office from 1929 to 1933.
His mandate was marked by the disastrous crisis of the 29th.
The Herbert Hoover's statistics like age, body measurements, height, weight, bio, wiki, net worth posted above have been gathered from a lot of credible websites and online sources. But, there are a few factors that will affect the statistics, so, the above figures may not be 100% accurate.


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Stepping up the ranks
Kim Bolan
Young Indo-Canadian gangsters are becoming increasingly sophisticated, and adopting names and logos like the infamous outlaw motorcycle clubs, police say.
A year ago police felt that Indo-Canadian gangs, despite dozens of murders, were less organized than traditional crime groups. But today there is a level of sophistication exhibited by these rival groups as they tussle over turf in B.C.'s lucrative drug trade.
The RCMP's annual report on organized crime this year ranks the Indo-Canadian groups third after outlaw bikers and Asians in terms of their strength and organization in B.C.'s hierarchy of criminal organizations.
CREDIT: Peter Battistoni, Vancouver Sun
In what has become the standard memorial to an accident victim, flowers and other items are left at the Marine and Main site where Sukvinder Singh (Bicky) Dosanjh died in a collision.
And the killing of gang members has continued, with 10 murders since last fall of Indo-Canadians or their associates linked to gangs.
The latest victim, Hardev Singh Sidhu, 27, was found slumped in his car at 136th Street and Grosvenor Road in Surrey early Friday morning.
Dozens of other drive-by shootings have been investigated by police in Abbotsford, Surrey, Vancouver and elsewhere, including a second Surrey shooting early Friday outside a pub.
The most disturbing trend, say police, is the increased organization of some Indo-Canadian gangsters, such as a Vancouver-based group calling itself the Independent Soldiers, and battling rival groups involved in drug trafficking.
On Sept. 10, Vancouver police were called to the downtown nightclub Tonic where members of the Independent Soldiers and the Abbotsford-based UN gang attacked each other with bar stools and broken bottles.
Two men were taken to hospital with injuries, but did not cooperate with police. No charges were laid.
Independent Soldiers' kingpin Sukhvinder Singh (Bicky) Dosanjh was killed in a car accident at Marine and Main Street two weeks ago, leaving a void in the evolving organization with links going back to notorious cocaine dealer Bindy Johal.
Dosanjh, a graduate of John Oliver secondary, is the brother of Gerpal Singh (Paul) Dosanjh, who was gunned down in March 2004 at the Gourmet Castle Restaurant in the 2800-block of East Hastings and who was also involved in the drug trade.
Paul Dosanjh had survived being shot in the head in August 2003.
The Dosanjh brothers are first cousins of Ron and Jimmy Dosanjh, among the original group of Indo-Canadian gangsters who were taken out in separate hits in 1994 and 1995. The high-profile murders were believed to have been arranged by Bindy Johal, their former associate-turned-rival in the cocaine trafficking world.
Johal was then murdered on the dance floor of a Vancouver nightclub in December 1998 in a targeted hit arranged by his former associate Bal Buttar. Buttar remains a blind quadriplegic after an attempt on his life in August 2001 by members of his own crew.
Vancouver police staked out Bicky Dosanjh's funeral last Saturday at Hamilton Harron Mortuary on Fraser Street where dozens of young men with gang links came to pay their respects to the dead gangster and former high school basketball star.
Vancouver police Insp. Kash Heed said the trend to more organized Indo-Canadian crime groups is disturbing.
"You are starting to see them identifying themselves in a similar way to gangs in the United States," Heed said. "Now you have Indo-Canadian gang clothing with identifiable logos."
But police and Indo-Canadian community groups are also evolving in their response to the Indo-Canadian violence. Ten months ago, the B.C. government committed tens of millions of dollars to the new B.C. Integrated Gang Task Force, which is targeting the violence among young Indo-Canadian gangsters that has led to dozens of murders in the last decade.
Independent Soldiers' kingpin Sukvinder Singh (Bicky) Dosanjh, who died two weeks ago, and the gang's emblem.
"We've had unbelievable cooperation from all the departments and agencies to put this together," Robin said in an interview. "Everyone's aware that this is a long-term commitment."
Robin said the task force is putting its effort into targeting violent individuals in groups who are currently active.
"What our purpose is is to target those individuals who are extremely violent," he said, adding that some on the list may be suspects in unsolved murders. "It takes probably more resources than one single department or detachment could put together."
Robin said the Indo-Canadian gangsters do not follow the model of true organized criminals "and in some ways that makes them more dangerous."
The new task force is gathering and coordinating intelligence on the Indo-Canadian gangs better than before, Robin said.
"That is one of the things we are really working hard on," he said.
But they are also involved in major criminal investigations.
"We are just scratching the surface. We are in here for the long term and none of us expect to turn this around overnight."
There have been several key arrests both in B.C. and Washington state related to Indo-Canadian organized crime.
Last April and May, several alleged Indo-Canadian gangsters were arrested in two separate kidnapping and unlawful confinement cases and are now facing a series of charges.
And in the U.S., an alleged ecstasy dealer and would-be politician named Ravinder Kaur Shergill was arrested after the Drug Enforcement Agency taped her in an undercover sting operation.
One of the most high-profile arrests was of Vancouver lawyer Kuldip Singh Chaggar, who was convicted in Seattle last April of tampering with a witness in a drug case involving alleged Indo-Canadian crime figures who were caught in a cross-border trafficking case.
Chaggar is now serving a year in jail, although he is appealing his conviction.
RCMP Insp. Paul Nadeau, head of the regional drug section, said the Indo-Canadians are primarily specializing in the transport of marijuana, with so many in the community involved in the commercial trucking industry. He said the Indo-Canadians are contracting to other crime groups to deliver their product.
Nadeau said that the use of commercial trucks to transport pot to the U.S. is up about 400 per cent over the last three years.
Jaskiren Sidhu, of the youth group UNITED, said it is disturbing to learn of the increasing sophistication of the Indo-Canadian crime groups.
But he said the Indo-Canadian community is taking steps to prevent further violence.
Groups like UNITED, VIRSA and others have been working with police and government to come up with strategies to combat the problem.
"For the first time, the police, the community and governments are coordinating their response in a very significant way," Sidhu said.
UNITED is doing mentoring and sports programs for youth and also working with a production company to develop anti-gang public service announcements.
"But there are no easy fixes. It is going to take a long time to reduce the level of violence and the power of the crime groups," Sidhu said.
The federal and provincial governments are committed to strategies to end the violence.
A 10-person committee of Indo-Canadian professionals is working on a report for the federal government, to be delivered this fall, on the Indo-Canadian gang problem.
Other groups are also working within the community to warn kids to stay away from gang life.
But there is still an attraction for youth to the mythic power of dead gangsters like the Dosanjhs and Bindy Johal, Heed said.
"Some youth looked up to these people and they still look up to these people as mentors," Heed said.
Proof of his belief are several websites still active where people spout on about which Indo-Canadian gangster they admire most. Bindy Johal still seems to get the most response, though other names of both dead and living Indo-Canadian crime figures are bandied about as heroes.
What has changed is that the Indo-Canadian community is taking ownership of the issue like never before, Heed said, with many groups being formed to steer young people away from gang life.
"We are starting to see little pockets of success, with several initiatives put in place in the last year," Heed said.
Vancouver police have been pro-active in following gang members to ensure they are not carrying weapons when they come downtown on a weekend to party.
"The message is if you come into Vancouver to party, you better behave," Heed said.
Vancouver nightclub shootings have been down in the last year, though there are still bar fights like the one that broke out Sept. 10.
Heed said that if Vancouver police become aware of a dispute between rival groups that could lead to an attempt on someone's life, officers get directly involved.
"We will go to the parents of these individuals and tell them what is going on," Heed said.
Parents do what they can to keep an eye on their kid.
"We have had significant success with this particular strategy.
But there are still problems.
Heed said there has been an "inordinate number of shots fired in southeast Vancouver," the neighbourhood where many of the Indo-Canadian gangsters still live.
"That is the area under my direct command. Fortunately, it has not resulted in any injuries," Heed said. "There have been shootings into vehicles, into houses or in the air. It is the bravado behaviour of individuals when they are out partying."
While much of the Indo-Canadian gang violence used to take place in Vancouver, it has shifted to cities east of downtown as the Indo-Canadian population has grown in those areas, Heed said.
Abbotsford and Surrey have had more of the killings in the last year and much of the gun action.
Vancouver police have also developed a graphic presentation on gang violence, which they have given to families, community leaders and "even to some youth at risk," Heed said.
Indo-Canadian Gang or Drug-Related Killings in the Last Year:
- Sept. 30, 2005 -- Hardev Singh Sidhu, 27, was found shot to death in a car at 136th Street and Grosvenor Road in Surrey. He is believed to have been involved in the drug trade.
- Aug. 28, 2005 -- Hartinder (Harry) Gill and his girlfriend Lexi Madsen were gunned down at a busy intersection in Abbotsford. Gill was facing an attempted murder charge at the time of his death and was well-known to police. His house was hit by gunfire in July.
- May 13, 2005 -- Surrey resident Dean Mohamed Elshamy, 30, was found slumped in a late-model grey Audi in the parking lot of a Mac's store at 72nd Avenue and Scott Road in Surrey. While Elshamy is Egyptian, the intended target of the hit is believed to have been his buddy, Sandip Singh Duhre, who was uninjured in both the May shooting and a second incident in July 2005.
- May 7, 2005 -- Inderjit Singh Rai, 23, shot to death about 2:30 a.m. in the 9800-block 140th Street in Surrey.
- April 2, 2005 -- Sukh Jawanda, killed on a rural road in Abbotsford. His friend was injured in the shooting.
© The Vancouver Sun 2005