text:
\section*{Abstract}
{\bf

  We use a mobile impurity or depleton model to study elementary excitations
  in one-dimensional integrable systems.  For Lieb-Liniger and bosonic
  Yang-Gaudin models we express two phenomenological parameters characterising
  renormalised interactions of mobile impurities with superfluid background:
  the number of depleted particles, $N$ and the superfluid phase drop $\pi J$
  in terms of the corresponding Bethe Ansatz solution and demonstrate, in the
  leading order, the absence of two-phonon scattering resulting in vanishing
  rates of inelastic processes such as viscosity experienced by the mobile
  impurities.}

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\section{Introduction}
\label{sec:intro}

Currently there is an ongoing interest in physics beyond Luttinger Liquid in
one-dimensional systems \cite{Imambekov2012}.  An example of such behaviour is
provided by systems featuring mobile impurities, representing one or few particles
moving in a correlated background liquid. This situation
was recently realised in ultra-cold atoms by either using atoms
in different hyperfine states
\cite{Koehl_PhysRevLett.103.150601,Fukuhara2013,Meinert2016} or by creating a
highly imbalanced mixture of different atoms
\cite{Catani2012,Spethmann2012a}. By exploiting unprecedented control over
parameters of the underlying Hamiltonian these experiments have uncovered rich
dynamics of mobile impurities and have revived interest in their theoretical
studies either in the context of liquid helium
\cite{LandauKhalatnikov1949ViscosityI,LandauKhalatnikov1949ViscosityII,BaymEbner1967Phonon}
or, more recently, in the context of one-dimensional quantum liquids
\cite{Neto1994,castro96}.

There are two main types of questions one can ask about these systems. The
first one concerns  dissipative dynamics of mobile impurities resulting
from the strong coupling to environment
\cite{zvonarev_2007,Gangardt09,Schecter_Gangardt_Kamenev_2012,Schecter2012a,Schecter2016,Matveev2012a,Mathy2012,Knap2014,Peotta2013},
while the second type of questions deals with correlation properties of quantum
liquids affected by the presence of mobile impurities
\cite{Tsukamoto1998,Zvonarev_etal_PhysRevB.80.201102,Kamenev08}. These
questions can be extended to one-component quantum liquids as their
high-energy nonlinear excitations, like solitons, can be described as
effective mobile impurities
\cite{Khodas2008PhotosolitonicEffect,Gangardt2010Quantum}.

Theoretically, the physics of mobile impurities is modelled by a single
localised degree of freedom coupled to an extended environment.  For
sufficiently low temperatures and weak external fields the latter is only
slightly perturbed so it can conveniently be represented by a collection of
phonons in the form of Luttinger Liquid (LL)
\cite{LutherPeschel1975,Popov1980,HaldanePRL81,Haldane1981Luttinger,GiamarchiBook}.
The coupling between the localised impurity and LL can be characterised by
only two parameters: the number of background particles, $N$, expelled from
the vicinity of impurity and the phase drop, $\pi J$, of the local superfluid
order parameter.  The existence of these parameters, called collective charges
below, is attributed to the existence of two local conservation laws: the
conservation of number of particles and conservation of momentum. The length
scale separation between localised impurities and extended phonons allows for
extraction of the values of collective charges from the response of the
equilibrium dispersion relation $\varepsilon (k)$ of impurity-like excitations
to small changes in background density and velocity fields and leads to a
phenomenological  depleton model
\cite{Schecter_Gangardt_Kamenev_2012,Schecter2016}
for which $\varepsilon(k)$ is the only physical input.

This model was successful in predicting the rate of momentum exchange between
the moving impurity and the phononic bath giving rise to viscous friction
experiences by impurities \cite{Neto1994,castro96,Gangardt09}.
A slightly different, but equivalent  approach was used
for determining relaxation rates toward thermal
equilibrium in one dimensional systems due to mobile impurities
\cite{Matveev2012a,Matveev2012}.

On the other hand, the contribution of mobile impurities to correlation
functions leads to power law singularities near the excitation threshold
$\varepsilon (k)$ \cite{Imambekov2012}.  It can therefore be expected that the
corresponding edge exponents are determined by the same collective charges
characterising the impurity-background interactions in the depleton model.
The relation can indeed be established using the method of Kamenev and Glazman
\cite{Kamenev08}  based on Ref.~\cite{BaymEbner1967Phonon} for extracting the
edge exponents from the magnon dispersion of a general Galilei invariant spin
liquid.  The method was further developed in Ref. \cite{Imambekov2009b} for a
variety of Galilei invariant bosonic or fermionic models.
A similar calculation based on the equilibrium dispersion
$\varepsilon (k)$, as we show below, leads to the collective charges of
Ref.~\cite{Schecter_Gangardt_Kamenev_2012}, thus establishing their connection
to the correlation properties of one-dimensional quantum liquids with mobile
impurities.

For a general interacting system, the dispersion relation $\varepsilon (k)$
which determines both dynamics and correlations in systems with mobile impurities
can be either calculated analytically using an appropriate perturbation
scheme or obtained numerically.  There exist, nonetheless, a class of exactly
solvable one-dimensional systems, where the dispersion of excitations is known
exactly in terms of Bethe Ansatz solution
\cite{Korepin1993}. Important examples of such systems include Lieb-Liniger
model \cite{Lieb1963} of bosons interacting via a delta function potential and
the closely related bosonic Yang-Gaudin model \cite{CN_Yang_1967,Gaudin_1967} of
interacting spin one-half bosons.

The goal of this paper is to treat excitations of Lieb-Liniger and bosonic
Yang-Gaudin models as mobile impurities and find their collective charges in
terms of the corresponding Bethe Ansatz solutions. We were able to express
collective charges directly in terms of shift functions (otherwise known as
dressed phases in BA literature) of elementary excitations.  This result
reproduces the conjectured identity of chiral linear combinations of the
collective charges, so called chiral phase shifts, with BA shift functions
\cite{Zvonarev_etal_PhysRevB.80.201102,Imambekov2009b,Cheianov2008,Imambekov08}.  Recently,
the calculation of correlation functions in Lieb-Liniger model by the
form-factor approach by Kitanine \emph{et al.} \cite{Kitanine2012} confirmed
the expression of the edge exponents in terms of BA shift functions obtained
in \cite{Imambekov08}.

The expression of the collective charges in terms of BA shift functions allows
us to find a very useful and transparent representation for $N$ and $J$ in
terms of derivatives of the excitation's momentum with respect to BA
parameters, see Eq. (\ref{eq:NJbeautiful}) and (\ref{eq:NJmagnonbeautiful})
below. These identities lead straightforwardly to exact vanishing of the
phononic back scattering amplitude in the leading, two-phonon, order.  This
result should not come as a surprise given the exact integrability of the
models, but it is far from obvious in the phenomenological approach based
on mobile impurities. Up to now it  could only be verified in a number of
particular cases of weak and strong interactions
\cite{Gangardt09,Gangardt2010Quantum}.

The paper is organised as follows. In Section~\ref{sec:collcharge} we review
the depleton model containing collective charges $N$ and $J$ and give their
expression in terms of the dispersion $\varepsilon (k)$. We demonstrate
the relation between the collective charges and chiral phase shifts
and use it to reinterpret various edge exponents  in terms of $N$ and $J$.
In Section~\ref{sec:BAcharges} we review BA
solution for elementary excitations of Lieb-Liniger and bosonic Yang-Gaudin
models. Then we obtain exact relations between  the collective charges  $N$ and
$J$ and solutions of BA equations  for  Lieb-Liniger model
in Section \ref{sec:derivatives} and for
bosonic Yang-Gaudin model in Section~\ref{sec:magnon_charges}.
Finally, we discuss in Section~\ref{sec:bscattering}   phononic  back
scattering amplitude and show that it vanishes
identically for these models.
We present conclusions and open questions   in
Section~\ref{sec:summconcl}. Technical details needed for the proofs
 are delegated into four Appendices for clarity.

\section{Depleton model, its collective charges and edge exponents of
  correlation functions near excitation thresholds}
\label{sec:collcharge}

Depleton model is designed to describe mobile impurities within path intgral
formalism and is defined by the action
$\mathcal{S}=\mathcal{S}_\mathrm{ph}+\mathcal{S}_\mathrm{d}$, where
\begin{align}
  \label{eq:sph}
  \mathcal{S}_\mathrm{ph} = -
  \frac{1}{\pi} \int \mathrm{d} t\mathrm{d} x
  \left(\partial_x \vartheta\partial_t\varphi+\frac{v_\mathrm{s}K}{2} \left(\partial_x\varphi\right)^2
    +\frac{v_\mathrm{s}}{2K} \left(\partial_x\vartheta\right)^2\right)\, ,
\end{align}
describes extended environment by using the slow hydrodynamic fields
$\varphi(x,t)$ and $\vartheta(x,t)$. The latter is related to density as
$n(x,t)=n+\rho(x,t) = n+\partial_x\vartheta/\pi$, where $n$ is the equilibrium density.
Correspondingly, the field $\varphi (x,t)$ describes the superfluid phase and
is  canonically conjugated to $\rho(x,t)$.
The Luttinger Liquid action, Eq.~(\ref{eq:sph}), describes phonons with linear dispersion
relation $\omega=v_\mathrm{s}|k|$, where $v_\mathrm{s}$ is speed of sound.
The relative magnitude of fluctuations of the fields $\varphi$ and $\vartheta$
are controlled by the Luttinger parameter $K=\pi n/mv_\mathrm{s}$, where $n $
is the average density and $m$ is the mass of the background  atoms.

To describe a localised object with coordinate  $X(t)$  and the canonically
conjugate momentum $P(t)$ we consider action
\begin{align}\
  \label{eq:sd}
  \mathcal{S}_\mathrm{d} = \int \mathrm{d} t \,\Big( P \dot X - H (P,N,J)  - \dot N\varphi (X,t) - \dot{J}
  \theta (X,t)\Big) .
\end{align}
This action describes a sharp ``kink'' in the smooth configuration of the
hydrodynamic fields located at $X(t)$ and parametrised by collective charges
$N(t)$ and $J(t)$.   The depleton charge $N(t)$ represents the number
of background particles expelled from  the vicinity of the depleton, therefore
$\pi N(t) $ is the magnitude of the ``kink'' in the otherwise smooth
configuration of $\vartheta$. Similarly, $\pi J(t)$ is the size of the
``kink'' in $\varphi$.  In the absence of phonons, the charges take their
equilibrium values $N(t)=N$, $J(t)=J$ obtained from the condition
$\partial H/\partial N = \partial H/\partial J =0$. The dispersion relation is the equilibrium
value of the energy $H(P,N,J) =\varepsilon(P)$. It was shown in
\cite{Schecter_Gangardt_Kamenev_2012} that the equilibrium collective charges
are given directly in terms of the
dispersion\footnote{Ref.\cite{Schecter_Gangardt_Kamenev_2012} uses notations
  $N,\Phi$, where  $N$ has the same meaning as in this paper and $\Phi = \pi J$.},
\begin{eqnarray}\label{eq:NJdisp1}
N &=& \frac{1}{v^2(k)-v_\mathrm{s}^2} \left( \frac{v_\mathrm{s}K
  }{\pi}\frac{\partial \varepsilon (k)}{\partial n} + \frac{k}{m}v(k)\right)\\
\label{eq:NJdisp2}
J &=& \frac{1}{v^2(k)-v_\mathrm{s}^2} \left( \frac{v(k)}{\pi}
  \frac{\partial \varepsilon (k)}{\partial n}  +
  \frac{v_\mathrm{s}}{K}\frac{k}{m}\right) \, .
\end{eqnarray}
Here $v(k) =
\partial\varepsilon(k)/\partial k$ is the velocity of the excitation.

In addition to describing dissipative dynamics of mobile impurities
\cite{Schecter_Gangardt_Kamenev_2012,Schecter2016} the depleton action
$\mathcal{S}$  can be used to calculate leading power law behaviour
of various correlation functions the vicinity of the excitation threshold
$\omega\sim\varepsilon(k)$ as shown in Appendix~\ref{sec:depl}.
In this case the path integral is dominated by the stationary value
of the action $\mathcal{S}$ which becomes logarithmically
large and leads to the  power-law behaviour
$\sim |\omega-\varepsilon(k)|^{-\mu}$, where the edge exponent
 \begin{align}
   \label{eq:beta}
   \mu
   =1- 2K\left[\left(\frac{N}{2K}\right)^2+\left(
       \frac{J}{2}\right)^2\right]\,
 \end{align}
is determined by the equilibrium values of the collective charges
(\ref{eq:NJdisp1}),~(\ref{eq:NJdisp2}).

The collective charges $N$ and $J$ can be connected with
the parameters $\delta_\pm $, called chiral phase shifts, of the unitary
transformation in the standard calculation \cite{Imambekov2012} of the
correlation functions using the X-ray edge approach
\cite{Nozieres1969,Mahan1981,Ohtaka1990}.  In the latter,
the chiral phase shifts characterise the discontinuities
in the chiral phononic fields $\chi_\pm = \vartheta/\sqrt{K} \pm
\sqrt{K}\varphi$
created by boundary condition changing operators
\cite{Schotte1969,Affleck94}.  The charges $N,J$, on the other hand,
characterise the discontinuities in the fields $\vartheta$ and $\varphi$.
The simplest way to establish connection between
these two sets of parameters is  by comparing
Eqs.~(\ref{eq:NJdisp1}),~(\ref{eq:NJdisp2})
with those  of the phase shifts $\delta_\pm$
\begin{align}
\frac{\delta_{\pm}}{\pi}\pm \frac{1}{\sqrt{K}}
&=\frac{1}
{v(k)\mp v_\mathrm{s}}\left(\frac{\sqrt{K}}{\pi}\frac{\partial\varepsilon(k)}{\partial n}\pm  \frac{1}{\sqrt{K}}\frac{k}{m}\right)\label{deltas}
\end{align}
first obtained in Ref.~\cite{Kamenev08,Imambekov2009b} in terms of the mobile
impurity dispersion relation. It is easy to see that the phase
shifts and the collective charges are related by
\begin{align}\label{deltaNJ}
 \frac{\delta_{\pm}(k)}{\pi}\pm \frac{1}{\sqrt{K}}
=\sqrt{K} J \pm \frac{N}{\sqrt{K}}
 \, .
\end{align}

The expression  (\ref{eq:beta}) reproduces known results
for edge exponents if  rewrite it in terms of the chiral phase shifts as
\begin{align}
\label{eq:mu12}
  \mu  &= 1-\frac{1}{2}\left(\frac{1}{\sqrt{K}} +
      \frac{\delta_+-\delta_-}{2\pi}\right)^2 -
    \frac{1}{2}\left(\frac{\delta_++\delta_-}{2\pi}\right)^2   \nonumber
  \\   &=1-\left(\frac{\delta_+}{2\pi}+\frac{1}{2\sqrt{K}}\right)^2 -
    \left(\frac{\delta_-}{2\pi}-\frac{1}{2\sqrt{K}}\right)^2\, .
\end{align}
The first line  reproduces exactly the results for the edge exponents
$\mu_{1,2}$  of Dynamic Structure Factor (DSF) of  interacting bosons,
 Eq.~(16) of Ref.~\cite{Imambekov08}, while the second line is
Eq.~(13) of Ref.\cite{Kamenev08} for the exponent $\mu_m$ of Dynamic Spin
Structure Factor (DSSF) of a general spin one half quantum liquid.
To reproduce edge exponents  $\overline{\mu_\pm}$ of the spectral function
$A(k,\omega)$  in Ref.\cite{Imambekov08} one notices that  in this case,  in addition to creating a
depleton, one removes exactly one particle from
the system, so one have to replace the number of missing particles   $N$ by
$N+1$. In terms of the phase shifts $\delta_\pm$ this leads to
\begin{align}
\label{eq:omupm}
 \overline{ \mu_\pm} = 1-\frac{1}{2}\left(
      \frac{\delta_+-\delta_-}{2\pi}\right)^2 -
    \frac{1}{2}\left(\frac{\delta_++\delta_-}{2\pi}\right)^2   \, ,
\end{align}
which reproduces exactly Eq.~(17) of \cite{Imambekov08}.

Similarly, to calculate $\underline{\mu}_\pm$ one replaces $N$ by $N-1$, which
corresponds to adding one particle so that,
\begin{align}
\label{eq:umupm}
 \underline{ \mu}_\pm = 1-\frac{1}{2}\left(\frac{2}{\sqrt{K}}+
      \frac{\delta_+-\delta_-}{2\pi}\right)^2 -
    \frac{1}{2}\left(\frac{\delta_++\delta_-}{2\pi}\right)^2   \,
\end{align}
again in full accordance with Eq.~(18) of Ref.\cite{Imambekov08}.

The same logic applies for calculating the edge exponents away from the
fundamental zone $0<k<2\pi n$.
Consider the lower edge, the Lieb II mode
$\varepsilon(k) = \varepsilon_2(k)$ as an example. A remarkable fact with far
fetching physical consequences  is that  $\varepsilon_2(q)$
is a periodic function, $\varepsilon_2(q+2\pi n) = \varepsilon_2(q)$.
This is due to the fact that the  momentum difference
$2\pi n$  results from the  presence of additional uniform
background supercurrent and the corresponding
phase winding of $2\pi $. The energies of the state with the supercurrent and
without it are the same in the thermodynamic limit.
The additional phase winding $2\pi l$ ($l$ is an integer) affects the value of
$J$ and  can be   taken into account by the substitution  $J\to J-2 l$
in Eq~(\ref{eq:beta}) so that  the resulting  edge exponent becomes
\begin{align}
\label{eq:mu2}
  \mu_l    &= 1- 2K\left[\left(\frac{N(k)}{2K}\right)^2+\left(
       \frac{J(k)}{2}-l\right)^2\right] \nonumber\\
&= 1-\frac{1}{2}\left(\frac{1}{\sqrt{K}} +
      \frac{\delta_+-\delta_-}{2\pi}\right)^2 -
    \frac{1}{2}\left(\frac{\delta_++\delta_-}{2\pi}+2l\sqrt{K}\right)^2   \, ,
\end{align}
which is the bosonic version of Eq.~(87) of Ref.~\cite{Imambekov2012}.

Thus the expression (\ref{eq:beta})  obtained within the depleton formalism
nicely combines previous results on edge exponents of dynamical correlation
functions obtained using  the mobile impurity model.
The collective charges $N$ and $J$ entering this
expression can be obtained  from  phenomenological dispersion   of the
mobile impurity excitations by Eqs.~(\ref{eq:NJdisp1}),~(\ref{eq:NJdisp2}).
 Below we obtain the collective charges for integrable
models using excitation dispersion from their   Bethe Ansatz solutions.

\section{Bethe Ansatz solution and elementary excitations of Lieb-Liniger and
  bosonic Yang-Gaudin models}
\label{sec:BAcharges}

Up to now our discussion of the effective mobile impurity with dispersion
relation $\varepsilon(k)$ was purely phenomenological.  We now turn to the
models  where the dispersion relation and, consequently, the
parameters $N,J$ determining the edge exponents can be obtained
analytically by Bethe Ansatz.  We consider
 Lieb-Liniger model \cite{Lieb1963} describing
one-dimensional bosons interacting with a short-range potential
$V(x) = c\delta(x)$ which is arguably the most studied continuous model
solved by Bethe Ansatz. Generalising this model to two species of bosonic
particles of the same mass and equal interaction couplings leads to bosonic
Yang-Gaudin model \cite{CN_Yang_1967,Gaudin_1967}.  This model can be
conveniently formulated using effective spin $1/2$ particles. Its ground state
is fully polarised \cite{Eisenberg_Lieb_2002} and is identical to that of
Lieb-Liniger model. Below we present  main equations which allow us to
obtain dispersion relation $\varepsilon (k)$ used for calculation of the
collective charges. All results of this Section can be found in
Refs.~\cite{Korepin1993,gaudinbook} and are reproduced here to make presentation
self-contained.

The ground state of Lieb-Liniger model is characterised by the density of
quasi-momenta $\rho(\nu)$ found from the equation
\begin{equation}
\rho(\nu)-\frac{1}{2\pi}\int^q_{-q}  K(\nu-\mu) \rho(\mu) \, \mathrm{d}\mu
= \frac{1}{2\pi}\label{rho} \, .
\end{equation}
Here $K(\lambda) = \partial\theta/\partial\lambda =2c/(c^2+\lambda^2)$, where
$\theta(\lambda)=2 \arctan(\lambda/c)$
is the scattering phase shift. We use units in
which the mass of the particles is $m=1/2$ and $\hbar=1$. In these units
the coupling constant $c$ and quasi-momenta  $\lambda$ have dimensions
of velocity.

The ``Fermi momentum'' $q$  limits the support of the ground state
density and is  determined  from the normalisation condition
\begin{align}\label{eq:norm}
   \int_{-q}^q \rho(\nu) \mathrm{d}\nu = n \, .
\end{align}

The excitations of Lieb-Liniger model are in one to one correspondence with
those of free fermions  and consist of either a particle excited above
the Fermi sea (Lieb I), so its quasi-momentum $\lambda$ is constrained by $|\lambda|>q$ or
a hole (Lieb II) with $-q<\lambda<q$ \cite{Lieb_1963}. The difference from
free fermions is that the positions of the
ground state quasi-momenta  are shifted as a result of the excitation
and these shifts  contribute  collectively to momentum
and energy. This effect is characterised by  the
\emph{shift function} $F(\nu|\lambda)$ which obeys the equation
\begin{equation}
F(\nu | \lambda)-\frac{1}{2\pi}\int^q_{-q} K(\nu -\mu) F(\mu | \lambda)\,
\mathrm{d}\mu  = \frac{\theta(\nu-\lambda)}{2\pi}\label{Fb}\, .
\end{equation}
Taking the limit $\lambda\to \pm \infty $ and comparing with Eq.~(\ref{rho})
it follows  that $F(\nu |\pm\infty) = \mp\pi \rho(\nu)$.
The  shift function  represents the relative change
of the ground state quasi-momenta   $\delta\nu\rho(\nu)  = \mp ( F(\nu|\lambda
)  + \pi \rho(\nu))$ as a result of a particle/hole with
quasi-momentum  $\lambda$. Here and below
the upper sign  corresponds to a particle-like (Lieb I)  excitation
while the lower sign corresponds to a hole-like (Lieb II)  excitation.
Some useful properties of the   shift function $F(\lambda|\nu)$
are summarised in Appendix~\ref{sec:shift}.

The momentum and energy of Lieb I,II excitations are given by
\begin{align}
\label{eq:k}
  \pm k (\lambda) &=\lambda - \pi n- \int_{-q}^q F(\nu|\lambda)\,\mathrm{d}\nu \, , \\
\label{eq:eps}  \pm \varepsilon(\lambda) &=\lambda^2 - h -
2 \int_{-q}^q \mu  F(\mu|\lambda)\,\mathrm{d}\mu\, .
\end{align}
The integrals in the right hand side represent the collective contribution of
the displaced momenta in the ``Fermi sea''.  Eliminating $\lambda$ from
Eqs.~(\ref{eq:k}) and Eq.~(\ref{eq:eps}) leads to the dispersion relation
$\varepsilon(k)$.  Apart from momentum, the dispersion relation  $\varepsilon(k)$
depends on the density $n$ via the limiting momentum $q$ fixed by
normalisation (\ref{eq:norm}). The chemical potential $h$ is then fixed from
the condition $\varepsilon(q)=\varepsilon(-q)=0$.  As both signs in
Eq.~(\ref{eq:k}) should provide the same result for $\lambda=q$, it is clear
that $k(q)=0$. Since for a hole the momentum increases with decreasing
$\lambda$ one can show that $k(0)=\pi n$ and $k(-q)=2\pi n$. For a particle
$k(-q) = -2\pi n$.  There is an alternative way to express the momentum,
\begin{eqnarray}
\pm k(\lambda)&=& \lambda - \pi n +\int^q_{-q}\theta(\lambda- \nu)
\rho(\nu)\, \mathrm{d}\nu \, . \label{eq:k1}
\end{eqnarray}
Similarly, the energy of excitations $\epsilon(\lambda) = \pm \varepsilon (\lambda)$  for particles ($|\lambda| > q$) / holes ($|\lambda| > q$)  can be found from the equation
\begin{eqnarray}
\epsilon(\lambda)&-&\frac{1}{2\pi}\int_{-q}^{q}
K(\lambda-\mu)\epsilon(\mu)\,\mathrm{d}\mu= \lambda^2- h \, .\label{eq:eps1}
\end{eqnarray}
The  equivalence of
(\ref{eq:k1}),~(\ref{eq:eps1}) and (\ref{eq:k}),~(\ref{eq:eps})  was first
demonstrated in Ref.~\cite{Korepin1993}. We reproduce it for convenience
in Appendix~\ref{sec:resolvent}.

In the bosonic Yang-Gaudin model in addition to Lieb I,II excitations
there is another type of excitations corresponding to
a spin flip of one of the particles. The flipped spin particle is
introduced with quasi-momentum $\lambda$ causing the
change in the quasi-momenta $\delta\nu\rho(\nu) = \tilde F(\nu|\lambda) +
\pi\rho(\nu) $. The  shift function $\tilde
F(\nu|\lambda)$ is found from the equation
\begin{equation}
\tilde F(\nu | \lambda)-
\frac{1}{2\pi}\int^q_{-q} K(\nu -\mu) \tilde F(\mu | \lambda)\,
\mathrm{d}\mu  = \frac{\theta(2\nu-2\lambda)}{2\pi}\label{Ft}\, .
\end{equation}
This equation differs from  Eq.~(\ref{Fb}) by the factor two in the argument
of the bare phase shift.
The momentum of the magnon excitation is obtained by the shift of the
ground-state quasi-momenta
Eqs.~(\ref{eq:k}),~(\ref{eq:k1})
\begin{align}
  \label{eq:ks}
\tilde k(\lambda)&=\pi n +\int_{-q}^q \tilde F(\nu|\lambda)\mathrm{d}\nu
            =\pi n + \int_{-q}^{q}
  \rho(\nu)\theta(2\nu-2\lambda)\mathrm{d}\nu
\end{align}
The last equality  follows from Eq.~(\ref{Ft}).
The corresponding energy of a magnon can be similarly expressed as
\begin{align}\label{eq:es}
  \tilde\varepsilon(\lambda)&=2 \int_{-q}^q \nu \tilde F(\nu|\lambda)\mathrm{d}\nu=\frac{1}{2\pi} \int_{-q}^q
               \partial_\nu \epsilon (\nu) \theta(2\nu-2\lambda)\mathrm{d}\nu
            =-\frac{1}{\pi} \int_{-q}^q \epsilon (\nu) K(2\nu-2\lambda)\mathrm{d}\nu \, ,
\end{align}
where $\epsilon$ is the solution of Eq.~(\ref{eq:eps1}) and
the last equality is obtained by integrating by parts.

\section{Collective charges and shift functions in integrable models}
\label{sec:derivatives}

The parametric expressions (\ref{eq:k}),~(\ref{eq:eps}) and
(\ref{eq:ks}),~(\ref{eq:es}) of the previous section allows us to obtain the
dispersion relations of excitation $\varepsilon(k)$ in Lieb-Liniger and
$\tilde\varepsilon(\tilde k)$ in bosonic Yang-Gaudin models in terms of shift
functions $F(\nu|\lambda)$ and $\tilde F(\nu|\lambda)$ correspondingly.  It is
therefore expected that the same Bethe ansatz shift function determine the
collective charges  $N,J$ or their chiral combinations $\delta_\pm(k)$.
Indeed, the previous studies
\cite{Imambekov08,Zvonarev_etal_PhysRevB.80.201102} suggested the following
particularly simple and physically appealing relation
\begin{align}
  \label{eq:delta_F}
  \frac{\delta_\pm (k) }{2\pi} = F(\pm q| \lambda(k))+\pi\rho(\pm q)\,
\end{align}
for excitations of Lieb-Liniger model and a similar expression for magnon
excitation of bosonic Yang-Gaudin model.  The conjecture (\ref{eq:delta_F}) is based
either on identification of $\delta_\pm (k)$ with the parameters of a boundary
changing operator of background particles \cite{Imambekov08} or on comparing
the finite size spectra
\cite{Pereira2008,Pereira_etal_PhysRevB.79.165113,Cheianov2008,Zvonarev_etal_PhysRevB.80.201102}.
To the best of our knowledge, the direct proof of Eqs.~(\ref{eq:delta_F})
for integrable models is still lacking and the consistency
of the thermodynamic definition Eq. (\ref{deltas}) with the relation
based on BA shift functions was established only numerically.
It should be noted, however, that the relation (\ref{eq:delta_F}), being
substituted into Eq.~(\ref{eq:beta}) leads to the edge exponent
identical\footnote{there is  overall minus sign due to a different definition
  of the edge exponent. Note also the difference in our definition of BA shift
functions and the one used in Ref.~\cite{Kitanine2012}.} to that obtained within the form-factor method in
Ref.~\cite{Kitanine2012}.

Below we provide the  direct proof of Eq.~(\ref{eq:delta_F}).
In the Subsection~\ref{sec:LLmod}
we deal with Lieb I and II  excitations of Lieb-Liniger model.
The relation similar to Eq.~(\ref{eq:delta_F}) for
bosonic Yang-Gaudin model is stated and
demonstrated in Subsection~\ref{sec:magnon_charges}.

\subsection{Lieb I and II excitations of Lieb-Liniger model}
\label{sec:LLmod}

Our proof is based on the following expressions for the
the derivatives of the dispersion relation    with
respect to the  ''natural'' parameters  $\lambda$ and $q$.  Defining for
simplicity  $F_\pm = F(\pm q|\lambda)$ we show in
Appendices~\ref{sec:thermo},\ref{sec:res1}  that
\begin{align}
    \label{eq:derqeps}
  \partial_q\epsilon (\lambda)  &=
  -v_\mathrm{s}\left(1+\sqrt{K}
                              \left(F_+-F_-\right)\right)\, ,
\end{align}
and
\begin{align}
\label{eq:derlambdaeps1}
  \partial_\lambda \epsilon (\lambda) &= \pm 2k(\lambda) +2\pi n
  \left(1+\frac{1}{\sqrt{K}}\Big(F_++F_- \Big)\right)  \, .
\end{align}
We also show there that
\begin{align}\label{eq:dkdq}
 \pm \partial_q k =-K\left(1+ \frac{1}{\sqrt{K}}\Big(F_++F_-\Big)\right)\,
\end{align}
and by
differentiating both sides of Eq.~(\ref{eq:k1}) and comparing
the result with Eq.~(\ref{rho}) we have
\begin{align}\label{eq:dkdlambda}
 \pm  \partial_\lambda k (\lambda) = 2\pi \rho(\lambda) = 1+F(\lambda|q)
  -F(\lambda|-q)\, ,
\end{align}
where we have used Eq.~(\ref{eq:id1}). We will also need the relation
\begin{align}\label{eq:dndq}
  \partial_q n =\frac{K}{\pi}\, .
\end{align}
proven in Appendix \ref{sec:resolvent}.

We transform the derivatives (\ref{eq:derqeps}),~(\ref{eq:derlambdaeps1})
of the dispersion relation  with
respect to the natural variables $\lambda$ and $q$ to those
with respect to density $n$ and momentum $k$. This can be achieved using
Eqs.~(\ref{eq:dkdq}), (\ref{eq:dkdlambda}) and~(\ref{eq:dndq}). Re-introducing
the particle's mass $m$ and going back to $\varepsilon=\pm \epsilon$ for
particles/holes we rewrite
Eqs.~(\ref{eq:derqeps}),~(\ref{eq:derlambdaeps1}) as
\begin{align*}
  \partial_\lambda \varepsilon &=\frac{k}{m} \pm v_\mathrm{s}\sqrt{K}
  \left(\sqrt{K}+F_++F_-\right)
  = \partial_\lambda k\,  \partial_k\varepsilon =
                             \pm v(k) \left(1+\sqrt{K}\left(F_+-F_-\right)\right)  \\
  \partial_q \varepsilon &=\mp v_\mathrm{s} \left(1+\sqrt{K}\left(F_+-F_-\right)\right)
  =
  \partial_q n \,\partial_n\varepsilon +\partial_q k \,\partial_k\varepsilon =
  \frac{K}{\pi} \partial_n\varepsilon \mp v(k) \sqrt{K}
    \left(\sqrt{K} + F_++F_-\right)\, .
\end{align*}
If one identifies in these equations, accordingly to Eq.~(\ref{eq:delta_F}),
the combinations
 \begin{align*}
   \frac{\delta_++\delta_-}{2\pi} &= 2\pi \rho(q) + F_+ +F_-
   = \sqrt{K} + F_++F_-\\
   \frac{\delta_+ - \delta_-}{2\pi} &=  F_+ - F_-
 \end{align*}
and solves for $\delta_\pm$ using the upper sign for particles
one obtains precisely Eqs.~(\ref{deltas}).

The  collective charges $N,J$ can be obtained using  Eq.~(\ref{deltaNJ}) with the
result
\begin{align}\label{eq:NF}
  N &= 1+\sqrt{K}\Big(F(q|\lambda)-F(-q|\lambda)\Big)
=1-F(\lambda|q)+F(\lambda|-q) = 2\pi \rho(\lambda) \\ \label{eq:JF}
  J &= 1+\frac{1}{\sqrt{K}} \Big(F(q|\lambda)+F(-q|\lambda)\Big) = 1-F(\lambda|q)-F(\lambda|-q)\, .
\end{align}
For $\lambda=\pm q$ we have $N= 2\pi\rho(\pm q) = \sqrt{K}=1/J$.

In the case of a hole-like Lieb II  excitation,  one has $k\to -k$,
$\varepsilon\to-\varepsilon$, but $v(k)=\partial\varepsilon/\partial k$ is  unchanged. The expressions
(\ref{eq:NJdisp1}),~(\ref{eq:NJdisp2}) become
\begin{eqnarray}\label{eq:NJdisp3}
N &=& \frac{1}{v_\mathrm{s}^2-v^2(k)} \left( \frac{v_\mathrm{s}K
  }{\pi}\frac{\partial \varepsilon (k)}{\partial n} + v(k) \frac{k}{m}\right)\\
\label{eq:NJdisp4}
J &=& \frac{1}{v_\mathrm{s}^2-v^2(k)} \left( \frac{v(k)}{\pi}
  \frac{\partial \varepsilon (k)}{\partial n}  +
  \frac{v_\mathrm{s}}{K}\frac{k}{m}\right) \, .
\end{eqnarray}

Comparing Eqs.~(\ref{eq:NF}),~(\ref{eq:JF})
with Eqs.~(\ref{eq:dkdq}) and (\ref{eq:dkdlambda})
 allows one to rewrite
the collective charges for both Lieb I (particles) and Lieb II (holes)
via partial derivatives of momentum $k(\lambda;q)$ as
\begin{align}\label{eq:NJbeautiful}
  N = \pm \frac{\partial k}{\partial \lambda}\, , \qquad J = \mp \frac{1}{K} \frac{\partial k}{\partial
  q}\, .
\end{align}
We are not aware of any previous studies discovering these nontrivial relations.

\subsection{Magnon excitation in bosonic Yang-Gaudin model}
\label{sec:magnon_charges}
For bosonic Yang-Gaudin model the phenomenological approach was used in
Ref.~\cite{Kamenev08} to express the phase shifts of the magnon excitation
in terms of the magnon momentum $\tilde{k}$ and
derivatives of the magnon dispersion relation $\tilde{\varepsilon}(\tilde{k})$ leading
to the result (\ref{deltas}) in which one replaces $k\to\tilde k$,
$\varepsilon\to \tilde\varepsilon$ and the group velocity  $v(k)\to
\tilde v(\tilde k) = \partial_{\tilde{k}}\tilde\varepsilon$. In  later work
\cite{Zvonarev_etal_PhysRevB.80.201102}
a relation between the phase shifts of the magnon
excitation and Bethe Ansatz shift function, similar
to Eq.~(\ref{eq:delta_F})  was proposed.
In the notation of Ref.~\cite{Kamenev08}, and using a slightly different sign
convention,
this   relation is given by
\begin{align}
  \label{eq:delta_Fs}
  \frac{\delta_\pm (k) }{2\pi}\pm \frac{1}{2\sqrt{K}}
  =- \tilde F(\pm q| \lambda(k))-\frac{\sqrt{K}}{2}\, .
\end{align}

To prove this  relation by analogy  to the case of the  Lieb-Liniger model
we need derivatives of the dispersion relation
\begin{align}\label{eq:depssdlam}
  \partial_\lambda\tilde\varepsilon &= \frac{ \tilde k (\lambda)}{m} -
  v_\mathrm{s}\sqrt{K}\left(\sqrt{K}+\tilde F (q|\lambda) +\tilde F(-q|\lambda\right) \\
\label{eq:depssdq}
  \partial_q \tilde\varepsilon &= v_\mathrm{s}\sqrt{K} \left(\tilde F (q|\lambda) -\tilde
  F(-q|\lambda\right)
\end{align}
and derivatives of the momentum
\begin{align}
\label{eq:dksdlam}
\partial_\lambda \tilde k&= - \sqrt{K} \left(\tilde F (q|\lambda) -\tilde
  F(-q|\lambda\right)    \\
\label{eq:dksdq}
\partial_q \tilde k & = \sqrt{K} \left(\sqrt{K}+\tilde F (q|\lambda) +\tilde
  F(-q|\lambda\right)  \,
\end{align}
proven in Appendix~\ref{sec:derYG}.
Substituting Eqs.~(\ref{eq:depssdlam}),~(\ref{eq:depssdq}),~(\ref{eq:dksdlam})
and (\ref{eq:dksdq}) into the following chain rules,
\begin{align*}
\partial_\lambda\tilde{\varepsilon} &= \partial_{\tilde{k}}\tilde{\varepsilon}\,
                                  \partial_\lambda \tilde{k}
                                  \, ,
  \\
\partial_q \tilde{\varepsilon} & = \partial_n\tilde{\varepsilon} \partial_q n  +
                             \partial_{\tilde{k}}\tilde{\varepsilon} \, \partial_q\tilde{k}
\end{align*}
and identifying the phase shifts via  Eq.~(\ref{eq:delta_Fs}) gives
\begin{align}
  \label{eq:delta_YG}
  \frac{\delta_\pm (k) }{\pi}&\pm \frac{1}{\sqrt{K}} =-\sqrt{K}J \mp
                                \frac{N-1}{\sqrt{K} }
=\frac{1}{\pm \tilde{v}\left(\tilde{k}\right)-v_\mathrm{s}}
\left(\frac{1}{\sqrt{K}}\frac{\tilde{k}}{m}
\pm\frac{\sqrt{K}}{\pi}\frac{\partial\tilde{\varepsilon}(\tilde{k})}{\partial
                                 n}\right)\,
\end{align}
in full agreement with the results of Ref.~\cite{Kamenev08}. The collective
charges are
\begin{align}\label{eq:Nmagnon}
  N
  &=\frac{1}{v_\mathrm{s}^2 -\tilde{v}^2\left(\tilde{k}\right)}
  \left( \frac{\tilde{k} - m \tilde{v}\left(\tilde{k}\right)}{m} \
    \tilde{v}\left(\tilde{k}\right)
  +\frac{K v_\mathrm{s}}{\pi} \left( \frac{\partial\tilde\varepsilon}{\partial n}
  +\frac{\pi v_\mathrm{s}}{K}\right)\right)\\  \label{eq:Jmagnon}
  J&=\frac{1}{v_\mathrm{s}^2 -\tilde{v}^2\left(\tilde{k}\right)}
  \left( \frac{v_\mathrm{s}}{K} \frac{\tilde{k}}{m}
   +\frac{\tilde{v}\left(\tilde{k}\right)}{\pi} \frac{\partial\tilde\varepsilon}{\partial n}
   \right)
\end{align}
as expected from  Ref.~\cite{Schecter_Gangardt_Kamenev_2012}.
Comparing Eqs.~(\ref{eq:NJdisp3}) and (\ref{eq:Nmagnon}) we see that there are
additional terms representing the bare momentum
$m\tilde{v}(\tilde{k})$ of the impurity and its chemical potential
$ \pi v_\mathrm{s} /K = mv_\mathrm{s}^2/n = \partial \mu/\partial n$. These
additional terms  cancel each other in Eq.~(\ref{eq:Jmagnon}) .

In  terms of the magnon shift functions, the collective charges are
\begin{align*}
  N &= 1+
  \sqrt{K}\left(\tilde{F}(q|\lambda) -\tilde{F} (-q|\lambda)\right)\\
  J &= 1+\frac{1}{\sqrt{K}} \left(\tilde{F}(q|\lambda) +\tilde{F}
      (-q|\lambda)\right)\, .
\end{align*}
Again, comparing these  expressions with
Eqs.~(\ref{eq:dksdlam}) and (\ref{eq:dksdq})
allows to rewrite the collective charges via partial derivatives of momentum
 as
\begin{align}\label{eq:NJmagnonbeautiful}
  N -1 = -\frac{\partial\tilde{ k}}{\partial \lambda}\, , \qquad
  J = \frac{1}{K} \frac{\partial\tilde{k}}{\partial q}\, .
\end{align}

\section{Phonon backscattering amplitude}
\label{sec:bscattering}

It was shown in Ref.~\cite{Schecter_Gangardt_Kamenev_2012} that the viscous
friction force acting on a moving impurity due to two-phonon processes is
proportional to the  squared absolute value of the phonon backscattering amplitude
$\Gamma_{+-}$. It is expected that in integrable systems this amplitude
vanishes due to the existence of infinitely many conservation laws. An example
supporting this statement is provided by a dark soliton, which is a hole-like
excitation of the Lieb-Liniger model in the weakly interacting regime and
which was shown to have infinite life-time in
Refs. \cite{Muryshev2002Dynamics,Gangardt2010Quantum}. Another example of a
non-decaying excitation is a spin-flipped particle (magnon) in bosonic Yang-Gaudin
model, as was shown in Ref.~\cite{Gangardt09} in the limit of weak and strong interactions.  Below
we prove that to the leading two-phonon order
the backscattering amplitude vanishes identically for
Lieb-Liniger and bosonic
Yang-Gaudin models for  \emph{any value of interactions}.

The expression for the back scattering amplitude was obtained in
Ref.~\cite{Schecter_Gangardt_Kamenev_2012} as the following combination
of partial  derivatives of the
collective charges
\begin{align}\label{eq:gamma}
  \Gamma_{+-} = \frac{\pi }{v_\mathrm{s}}\left(\left(N-\frac{M}{m}\right)
  \partial_{k} J -
     J \partial_{k} N - \frac{1}{\pi} \partial_{n}N \right)\ .
\end{align}
Here $M$ is the mass of the added impurity particle.
As it stands, Eq.~(\ref{eq:gamma}) is valid only
for subsonic excitations. In our case they are
the hole excitation of Lieb-Liniger model
for which $M=0$  since there is no additional particle
and the magnon of bosonic Yang-Gaudin model for which $M=m$.  For the supersonic
particle-like  excitation of Lieb-Liniger model the expression for the
back scattering amplitude must be modified as explained below.

We start with a hole-like  excitation for which $\Gamma_{+-}$  is  given
by
\begin{align}\label{eq:gammahole}
  \Gamma_{+-} = \frac{\pi }{v_\mathrm{s}}\left(  N\partial_{k} J -
     J \partial_{k} N - \frac{1}{\pi} \partial_{n}N \right).
\end{align}
We  convert the partial derivatives with respect to $k$ and $n$ into the
partial derivatives with respect to the ``natural'' variables using
\begin{align*}
  \partial_\lambda &= \frac{\partial k}{\partial \lambda} \partial_k = \pm 2\pi \rho (\lambda)
  \partial_k = \pm N \partial_k \\
  \partial_q &= \frac{\partial k}{\partial q}\partial_k +\frac{\partial n}{\partial q}\partial_n
  = \mp K \left( 1+\frac{1}{\sqrt{K}}
           \left(F(q|\lambda)+F(-q|\lambda)\right)\right)\partial_k +
           \frac{K}{\pi} \partial_n \\
  &=\mp KJ\partial_k +\frac{K}{\pi} \partial_n\, ,
\end{align*}
where we have
used Eqs.~(\ref{eq:NF}) and (\ref{eq:JF}).
Inverting the above expressions we get
\begin{align}\label{eq:derk}
  \partial_k &= \pm \frac{1}{N} \partial_\lambda \\
\label{eq:dern}
  \partial_n & = \frac{\pi J}{N} \partial_\lambda +\frac{\pi}{K}\partial_q\, ,
\end{align}
which can be used  (with the lower sign) in Eq.~(\ref{eq:gammahole}).
It leads to  a particularly simply looking  result
\begin{align}\label{eq:gammabeautiful}
  -\left(\frac{v_\mathrm{s}}{\pi}\right)  \Gamma_{+-} =
 \partial_\lambda  J + \frac{1}{K} \partial_q N =0\, ,
\end{align}
as a direct consequence of the relations  (\ref{eq:NJbeautiful}).

For the particle-like excitations (Lieb I mode) the expression
(\ref{eq:gammahole}) must be modified by replacing $N\to -N$ and $J\to -J$
(\emph{cf.}  Eqs.~(\ref{eq:NJdisp3}),~(\ref{eq:NJdisp4}) and
Eqs.~(\ref{eq:NJdisp1}),~(\ref{eq:NJdisp2})). In combination with the
upper sign in Eq.~(\ref{eq:derk}) this leads to
\begin{align*}
  \left(\frac{v_\mathrm{s}}{\pi}\right)  \Gamma_{+-} =
 \partial_\lambda  J + \frac{1}{K} \partial_q N =0 \ .
\end{align*}

Finally, for the magnon excitation of bosonic Yang-Gaudin model
we can simply replace $N$ by $N-1$ and $k$ by $\tilde{k}$
in Eq.~(\ref{eq:gammahole}), (\ref{eq:derk}),~(\ref{eq:dern}) and
(\ref{eq:gammabeautiful}).

\section{Summary and conclusions}
\label{sec:summconcl}

To summarise, we have obtained the collective charges $N$ and $J$ of mobile
impurities in integrable models directly in terms of the corresponding BA
shift functions.  Our method relies on the Bethe Ansatz solution which
provides a unique parametrisation of the elementary excitations in these
models by their rapidity as well as the parameter which limits the extent of
the ground state rapidity distribution.

This parametrisation is expressed via Bethe Ansatz shift functions and allows
for exact calculation of derivatives of the excitation energy with respect to
momentum and density which enter the phenomenological expressions for the
scattering phase shifts and collective charges found in earlier works.

As a byproduct we have found a novel expression for the collective charges of
the effective mobile impurity model in terms of the partial  derivatives
of the impurity momentum with respect to the Bethe Ansatz parameters mentioned
above.

A straightforward consequence of these relations is the absence of phonon
scattering off mobile impurities in the leading two-phonon order for all
values of interaction parameters. This absence was previously conjectured
based on approximate calculation in the limiting cases of weak and strong
interactions.  The proof of the expected  absence of inelastic processes beyond
two-phonon rate is an obvious extension of our work.

We expect that our methods  can be generalised to study excitations
in other models soluble by nested BA, such as, the fermionic Hubbard
model and integrable spin chains. The lack of
Galilean invariance in lattice models  can be dealt with following
techniques of Ref.\cite{Matveev2012a}.

redpajama_set_name: RedPajamaArXiv


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text:
Friedrich Ortloff (* 10. Oktober 1797 in Erlangen; † 10. Oktober 1868 in Jena) war ein deutscher Jurist, Professor und Präsident des Oberappellationsgerichts in Jena.

Leben
Friedrich Ortloff kam am 10. Oktober 1797 in Erlangen als Sohn des Schuhmachers und Philosophieprofessors Johann Andreas Ortloff und seiner Frau Anna Elisabeth Sophie Dürr zur Welt.

1803 zog sein Vater mit Familie nach Coburg, wo Friedrich Ortloff das Gymnasium von Coburg von 1809 bis 1814 besuchte. Nach der Schule studierte Friedrich Ortloff an den Universitäten Jena, Göttingen und Erlangen Jurisprudenz. Er war Mitglied der Erlanger Freimaurerloge Libanon zu den drei Cedern. In Coburg erhielt er 1816 mit 19 Jahren eine Anstellung als Advokat am Coburger Hofe und veröffentlicht 1818 seine erste Schrift Über die Erziehung zum Bürger und promovierte mit der Dissertation Commentatio juris romani de thesauris. 1819 im Alter von 22 Jahren folgte er einem Ruf als Professor für deutsches Privatrecht an der Universität Jena, mit der auch das Amt im Schöppenstuhl verbunden war, so dass Theorie und Praxis vereint wurden. Am Oberappellationsgericht Jena, das gemäß der Bundesverfassung im Jahre 1817 für die thüringischen Staaten eingerichtete wurde, wurde er 1826 als Rat berufen und fand nebenher Zeit, um als Honorarprofessor an der Jenaer Universität Vorlesungen zu halten, bis er 1844 mit relativ jungen 47 Jahren Präsident des Oberappellationsgerichtes wurde.

Als Präsident hatte Friedrich Ortloff seinen wesentlichen Anteil daran, dass die Rechtsprechung des Jenaer Oberappellationsgerichtes liberaler und fortschrittlicher als der anderer deutscher Obergerichte war. Nach der Revolution von 1848 war er an der Gesetzgebung beteiligt und arbeitete er in den Jahren 1848 und 1849 die Entwürfe für eine thüringische Strafprozessordnung und ein thüringisches Strafgesetzbuch aus, die 1850 in Kraft traten.

1856 beriefen die thüringischen Staaten Friedrich Ortloff zu ihrem Vertreter in der sächsisch-thüringischen Kommission zur Ausarbeitung des sächsischen Bürgerlichen Gesetzbuchs, an dem er maßgeblichen Anteil hatte. Vor allem im allgemeinen Teil und dem allgemeinen Schuldrecht wurden oft seine Entwürfe ohne Veränderung übernommen. Allerdings trat dieses Bürgerlicher Gesetzbuch nur in Sachsen, nicht aber in Thüringen in Kraft. Eine weitere Arbeit dieser Kommission war auch der Entwurf einer Zivilprozessordnung, die aber weder in Thüringen noch in Sachsen in Kraft trat.

Friedrich Ortloff starb am 10. Oktober 1868 im Alter von 71 Jahren in Jena. Er ließ einen Sohn aus erster Ehe und drei Kinder aus seiner zweiten Ehe zurück.

Bedeutung
Friedrich Ortloff hatte entscheidenden Anteil an der damaligen thüringischen liberalen Rechtsprechung und der sächsischen Zivilgesetzgebung. Seine Werke beschränkten sich oft auf das kritische Herausgeben und Zusammenstellen bisheriger Rechtsquellen. Sein wichtigstes Werk war wohl die Geschichte der Grumbachschen Händel in vier Bänden, welches die wichtigsten politischen Auseinandersetzungen in Thüringen in der zweiten Hälfte des 16. Jahrhunderts darstellte und damals als Standardwerk galt.

Werke
 Commentatio juris romani de thesauris, 1818
 Über die Erziehung zum Bürger, 1818
 Grundzüge eines Systems des Teutschen Privatrechts mit Einschluß des Lehnrechts, 1828
 Sammlungen deutscher Rechtsquellen, bestehend aus:
 * Das Rechtsbuch nach Distinktionen (Meißner Rechtsbuch/Ältere Eisenacher Rechtsbuch) 1836 und
 * Das Rechtsbuch Johann Purgoldts nebst statutarischen Rechten von Gotha und Eisenach, 1860
 Geschichte der Grumbach'schen Händel, 1868–70, 4 Bände

Literatur

 F. Wulfert: Das sächsische bürgerliche Gesetzbuch und die zur Revision des Held'schen Entwurfs eingesetzte Commission, in: Sächs. Archiv f. Bürgerl. Recht 1, 1891, S. 42–58; Stintzing-Landsberg;
 Ch. Ahcin: Zur Entstehung des bürgerlichen Gesetzbuchs für das Königreich Sachsen von 1863/65, 1996, S. 263–303.
 Hermann Ortloff: Dr. Friedrich Ortloff, wirklicher Geheimerath und Präsident des Gesammt-Oberappelationsgerichts zu Jena. Nekrolog. Friedrich Frommann, Jena, 1869 (Online)

Weblinks
 Grundzüge eines Systems des deutschen Privatrechts mit Einschluß des Lehnrechts von 1828 online
 Kurzer Lebensabriss

Rechtswissenschaftler (19. Jahrhundert)
Richter (deutsche Geschichte)
Hochschullehrer (Friedrich-Schiller-Universität Jena)
Ehrenbürger von Jena
Freimaurer (Deutschland)
Freimaurer (19. Jahrhundert)
Deutscher
Geboren 1797
Gestorben 1868
Mann

redpajama_set_name: RedPajamaWikipedia


text:
(function modifyArrayIterator() {
  'use strict';

  class Point {
    constructor(x, y) {
      this.x = x;
      this.y = y;
    }
  }

  class RestPoint extends Point {
    constructor(...args) {
      super(...args);
    }
  }

  function testRestPoint(x, y) {
    return new RestPoint(x, y);
  }
  testRestPoint(1, 2);
  testRestPoint(1, 2);
  % OptimizeFunctionOnNextCall(testRestPoint);
  var r = testRestPoint(1, 2);

  assertInstanceof(r, RestPoint);
  assertInstanceof(r, Point);
  assertEquals(1, r.x);
  assertEquals(2, r.y);

  Object.defineProperty(Array.prototype, Symbol.iterator, {
    value: function*
        () {
          yield 3;
          yield 4;
        },
    configurable: true
  });

  var r2 = testRestPoint(1, 2);

  assertInstanceof(r2, RestPoint);
  assertInstanceof(r2, Point);
  assertEquals(3, r2.x);
  assertEquals(4, r2.y);
})();

redpajama_set_name: RedPajamaGithub


Man Swallows Lightbulb Whole His boyfriend really loves watching him do this act.
Idiot Tries To Change A Light Bulb How many dumbasses does it take to change a light bulb?
Face First Through Florescent Bulbs Too bad hes probably not going to live long after getting all that mercury in him.
A Few Watts Short of A Lightbulb This lady is never going to live this one down. She should probably consider suicide.


Christian corporatism is a societal, economic, or a modern political application of the Christian doctrine of Paul of Tarsus in I Corinthians 12:12-31 where Paul speaks of an organic form of politics and society where all people and components are functionally united, like the human body. Christian corporatism has been supported by the Roman Catholic Church, Protestants, Christian democrats, and others. Economic application of Christian corporatism has promoted consultations between employers and workers and has sponsored Christian trade unionism.
During the Middle Ages, the Roman Catholic Church sponsored the creation of various institutions including brotherhoods, monasteries, religious orders, and military associations, especially during the Crusades to sponsor connection between these groups.
In 1881, Pope Leo XIII commissioned theologians and social thinkers to study corporatism and provide a definition for it. In 1884 in Freiburg, the commission declared that corporatism was a "system of social organization that has at its base the grouping of men according to the community of their natural interests and social functions, and as true and proper organs of the state they direct and coordinate labor and capital in matters of common interest."
In the aftermath of the Freiburg meeting, corporatism grew in popularity and the corporatist internationale was formed in 1890 followed by the publishing of Rerum novarum (1891) by the Roman Catholic Church that for the first time declared the Church's blessing to trade unions and called for organized labour to be recognized by politicians. Many corporatist unions in Europe were backed by the Roman Catholic Church to challenge the rise of anarchist, Marxist and other radical unions, with the corporatist unions being fairly conservative in comparison to their radical rivals.
On the fortieth anniversary of the publishing of Rerum novarum, Pope Pius XI in Quadragesimo anno (1931) advocated Christian corporatism as an alternative to capitalist individualism and socialist totalitarianism whereby people would be organized into workers' guilds or vocational groups that would cooperate under the supervision of a neutral state.
In response to the rise in popularity of Roman Catholic corporatism in the 1890s, Protestant corporatism arose, especially in the Germany, the Netherlands, and Scandinavia. However, Protestant corporatism has been far less successful in being supported by governments than its Roman Catholic counterpart.
1 2 Gehler, Michael and Kaiser, Wolfram, pp. 76.
1 2 Wiarda, Howard J., pp. 39.
↑ Wiarda, Howard J., pp. 31.
↑ Wiarda, Howard J., pp. 35.
↑ Wiarda, Howard J., pp.38.
↑ Peter Travis Kroeker. Christian ethics and political economy in North America: a critical analysis. McGill-Queens University Press, 1995. P94.
Gehler, Michael and Kaiser, Wolfram (2004). Christian democracy in Europe since 1945. New York, USA; Oxon: Routledge.
Wiarda, Howard J. (1997) Corporatism and comparative politics. M.E. Sharpe.


Description FPH1 is a small molecule that promotes the functional proliferation of primary hepatocytes.
The solubility of this compound in DMSO is >10 mM. General tips for obtaining a higher concentration: Please warm the tube at 37℃ for 10 minutes and/or shake it in the ultrasonic bath for a while. Stock solution can be stored below -20℃ for several months.
In primary human hepatocytes, FPH1 (BRD-6125) induced functional proliferation of hepatocytes and thus might be useful for expanding mature human primary hepatocytes. FPH1 induced an increase in hepatocyte nuclei count and/or elevated the number of nuclei undergoing mitosis in a concentration dependent way.
 Shan J, Schwartz R E, Ross N T, et al. Identification of small molecules for human hepatocyte expansion and iPS differentiation. Nature chemical biology, 2013.
FPH1 is a small molecule that promotes the functional proliferation of primary hepatocytes .
FPH1 belongs to the functional proliferation hits which are screened out by their ability to permit renewable sourcing of functional human hepatocytes. This ability of FPH1 is not dependent on the donors of the hepatocytes. It has been found that FPH1 was active against the primary human hepatocytes from six cell sources of genetically diverse individuals. Besides that, FPH1 can affect the hepatocyte functions with promoting albumin secretion during the differentiation of iPS cells into iHeps. Moreover, treatment of FPH1 also resulted in the increase of CYP3A4 levels and the decrease of AFP secretion .


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24 Addictive Free Linux Games (Part 1 of 3)
October 14, 2017 Steve Emms Games, Software
In recent months LinuxLinks Towers has been consumed with playing games. In fact, some might contend that game playing has become so excessive that real life has been neglected to a degree. We have seen team challenges, leaderboards, and even the odd wager. Healthy competition to say the least!
Many of the LinuxLinks crew grew up playing games on the ZX Spectrum, an 8-bit personal home computer. By today's standards, the games were simple with basic graphics plagued by attribute clash and primitive sound generation. However, this did not stop the best games being incredibly addictive. The famous Crash magazine (a monthly publication devoted to the ZX Spectrum) used to rate games by their addictive qualities. This was often the rating that interested us the most.
The purpose of this article is to identify some of our favourite free Linux games which have these addictive qualities. They may not offer breathtaking graphics, innovative ideas, or the highest presentation. However, what they do provide is great gameplay coupled with the urge of always having just one more play.
To be eligible for inclusion in this list each game needed to meet the following requirements:
Free to play (no download charge, no monthly charge)
Not in the early stages of development
This article is the first in a three part series.
Now, let's scrutinize the 8 games at hand. For each game we have compiled its own portal page, providing screenshots of the game in action, a full description of the game, with an in-depth analysis of the features of the game, together with links to relevant resources and reviews.
Addictive Free Games
Red Eclipse Single-player and multi-player first-person ego-shooter
Summoning Wars Network-based, role-playing game with a point-and-click fight system
XPilot NG Multiplayer 2D spacewar
Seven Kingdoms: AA Award winning real-time strategy game
FreedroidRPG Sci-fi isometric 3D role playing game
Frogatto & Friends Old-style platform game
Cave Story Side-scrolling platform game
Performous Karaoke game that allows user supplied songs
addictive gamesgamingsoftware
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Jason Derulo Tour Dates
Singer, songwriter, dancer, and actor Jason Derulo belongs to a new breed of multi-hyphenate artists who know no creative boundaries. He is now established as one of the world's biggest pop stars having sold over 30 million singles globally. Taking Michael Jackson as his biggest influence, along with comparisons to Usher and Flo Rida, Derulo's music is a hybrid of pop with R&B and hip-hop influences.
Jason Derulo tour dates listed on Ents24.com since Apr 2010.
Official website jasonderulo.com
Listen to Jason Derulo
Jun 27 Sun
Rock In Rio Lisboa 2021 Foo Fighters, The National, Liam Gallagher, Black Eyed Peas, Ivete Sangalo…
Lisbon, Parque Da Bela Vista
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It was a cold and windy day at Zwartkop Country Club, but the golf was still a big success.
We would like to welcome our new golfers Albano Dos Santos, Kobus Oeschger and Deon van Niekerk.
Winners in the disabled division: Herman van Wyk with 44 points and in 2nd place Bob Fussel on 39 points and in 3rd place Byron Calvert on 36 points.
Deaf division: Raymond Graaff with 33 points and in 2nd place Casper Geyer on 30 points and 3rd place Albano Dos Santos on 27 points.
Abled division: Reg Barry on 38 points.


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Campbell's Soup Company recently announced that it will replace Bisphenol A (BPA) with polyester or acrylic materials in its can linings. The company's transition to BPA-free can linings will be completed mid-2017.
In early March, Campbell started using cans with polyester or acrylic materials in the lining. The company said they will continue on this path in Canada and the United States until all their cans are switched to BPA-free ones.
By December 2016, approximately 75 percent of all Campbell's soup products will be BPA-free. By mid-2017, their other packaging such as V8 beverage aluminum cans and the glass jars' metal top lids will be BPA-free.
"Our priority throughout this transition has been, and will continue to be, food safety. We have tested and conducted trials with hundreds of alternatives to BPA lining and believe the acrylic and polyester options will ensure our food remains safe, affordable and tastes great," said Senior Program Manager, Packaging, Mike Mulshine in a company statement.
BPA is a common chemical used in the production of epoxy resins and polycarbonate plastics. These plastic materials have a wide range of applications including water bottles, food packaging, infant bottles, compact discs, medical devices and impact-resistant safety products.
BPA is used to line cans to prevent the food contents from corroding the metal. Unfortunately, BPA has been linked to several health conditions in recent years such as childhood obesity, tooth decay, asthma, miscarriage risks and even breast cancer.
BPA gets into the body mainly through diet. According to the U.S. National Institute of Environmental Health Sciences (NIH), BPA can seep into food contents from the cans' epoxy resins. It can also leach into food through the water bottles and storage containers.
"The degree to which BPA leaches from polycarbonate bottles into liquid may depend more on the temperature of the liquid or bottle, than the age of the container," said NIH.
Though the U.S. Food and Drug Association (FDA) said that low-dose BPA exposure is harmless, many consumers are still concerned about this toxic chemical and want it removed in the canned products.


Training Assessment What is your background and history with the sheet metal industry?
What CAD/CAM applications have you worked with and for how long?
What CAD system(s) are you aware of that your company uses?


Cocktails – we can create bespoke drinks to suit your budget, colour or a particular theme that you may have.
Corkage for your own wine – please email for all enquiries.
Corkage for your own Prosecco -please email for all enquiries.


1983 Honda Vt750 Shadow Wiring Diagram – Honda shadow 750 wiring diagram is just one of grown niche at the present time. We really hope it is simple to recognize it among your reference and lots of thanks for your effort for staying in our internet page. This book incorporates technical info, instructions for routine maintenance including oil change info, along with a simple troubleshooting guide. The engine is just like the'85 model. It is the same as the'84 model but with the right engine cover graphic not painted. It is the same as the'84 model with the right engine cover graphic painted black.
All the controls were light, handy and simple to use. The traction control and very low center of gravity would likewise aid in earning your ride secured and enjoyable. Not only do the 2 models look very similar, but they've been built with the very same components and total design. It isn't a consequence of defective manufacturing, therefore it's not covered by any warranty. It was the consequence of years of to tackle the requirements of the American industry.
The engineers developed an offset dual-crankpin design that provided perfect principal balance. The plan of the 2008 Honda Shadow bikes is among a classic American cruiser. Thus, the bars are likely to be absolutely the most universal fit for all models. Durability became a problem. The ride quality is quite comfortable. You are able to receive an array of news, ideas, articles, all around the world in only a few moments. It sports flawless lines, giving the concept of continuity together with the Shadow writing on the sides.
Lots of people have used on line to find information, hints, articles or some other guide for their demands. If anyone feels there's a need, I'll add all models to the chart. It includes all of the information that you will need to to have a fundamental comprehension of the operation of your automobile. Make sure you receive the information you're looking for. In todays modern era, information about the increase and development of technologies is extremely simple to grab.
It is possible to order your gaskets at the local Motor Cycle Dealer. The camchain sprockets also need to be loosened to permit extraction of the tensioners. The majority of Flanders handlebars arrive in Plain, and we list all of them. Once you've ensured your cruiser is running smooth, be certain your tire tread is where it has to be. The Power Cruiser was born.
A relaxing ride is among the ideal stress reliever we can think about. These bikes aren't for sale for a unit. In case the specific bike you're looking for parts for is not listed here, we don't have it. These were great bikes and there continue to be loads of them around they're so tough. This is a superb bike, particularly for beginners. Rest assured, our deals aren't restricted to tires! Our large choice of cruiser tires supply you with the chance to get the tire that most meets your needs.
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Putting the 'mam' in imam
Beijing is encouraging the spread of female imams among its Muslims
Erica Alini December 23, 2010
Pierre Bessard/REA/Redux
Communism, which preaches the equality of men and women, has done nothing to redress China's overweening cultural bias against baby girls, but it does seem to be helping women climb the social ladder in a rather unexpected place—the mosque. China, in fact, is the only country in the world with a tradition of female imams, a phenomenon that predates the advent of the People's Republic, but which the country's Communist government is helping to spread.
Women-only mosques and female preachers in China date back to the early 19th century, when they first appeared in the central provinces populated by the Hui, a Chinese Muslim group. Morocco also embraced the idea of female preachers in 2006, but the practice remains controversial in the Muslim world, and among many of China's own 21 million Muslims. Chinese women's mosques, though, found a helping hand in the government, which grants licences to practice Islam to both male and female imams through state-controlled bodies such as the Islamic Association of China. This kind of political backing is thought to be helping the spread of female-led mosques in areas of the country where women are still far from centre stage.
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FILED UNDER: China communism cultural bias female imams female preachers Islamic Association of China mosque muslims


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Home Culture Swanfall at the Ward Museum
Swanfall at the Ward Museum
Showcasing the swan's elegant lines and form are carvings, paintings, photography, and more at the debut mixed-media exhibit, Swanfall, taking place December 2nd through Fe uary 5th at The Ward Museum of Wildfowl Art in Salisbury.r
"Tundra swans were selected for a winter exhibit in part because the tundra swans spend their winters in the Chesapeake Bay area and although we have focused exclusively on other bird species, like crows, we have never featured an exhibit on swans before," says Dr. Cynthia Byrd, Ward Museum curator and folklorist.
In addition to featuring more than 40 swan-related works by 15 artists, the exhibit features "exclusive photography from Tom Horton and David Harp's book, Swanfall: Journey of the Tundra Swans, which explores the characteristics and behavior of swans. "The poetic style of the text and striking close-up photography appeal to audiences of all ages," explains Dr. Byrd.
While artists' works will be for sale, this is not a juried art show. Its goal is to provide the public a glimpse into the tundra swans migratory journey, folklore, and environment. The exhibit's opening reception takes place December 2nd from 5–7 p.m. and is free to the public. Attendees have the opportunity to meet the authors of Swanfall: Journey of the Tundra Swans at the Ward Museum Store. For more information visit wardmuseum.org or call 410-742-4988.
Arts+Entertainment In Print The Arts Year Issued: 2011 Month Issued: 11


Everyone was gone for the night and I had started to clean my office. Ever since I got a laptop a year ago, my office and desktop have been getting very neglected. At first you think "I'll just pull off a few keys and clean around them"……and before you know it, I had ALL of the keys off! Click the picture and take a look at all the GROSS crumbs, dirt even hair that was down in there! YUCK!!
So even though I was home alone and feeling lonely I had a pleasant surprise in my Inbox on Saturday morning!!! I was the winner (out of 234 entries!) of Bella Casa's Giveaway!!! Can I get a woot woot!! I won the Pillsbury Savorings Wine Swag Bag prize an awesome prize!!
Be sure to check out Bella's blog Bella Casa, she such a sweetie and has an awesome blog full of GREAT decorating ideas!!
This has been a lucky month for me!! Because I was also the winner on another FANTASTIC blog Cobblestone Farms. Remember my post about Cathy's GREAT giveaway? Well, I was the winner of a bag of her fall ornaments and bowl fillers!! How cool is that? Especially since I never got around to making any for myself (on my to-do list for next year). Be sure to check Cathy's blog – she takes such AWESOME pictures of all of her GORGEOUS flowers in such unique displays!! – I actually have this picture of hers as my desktop wallpaper!
Hope you had a HAPPY FALL WEEKEND!
You are very lucky , you know?? how about going to the casino with me one day? LOL Just kidding…glad to hear you won such lovely things! I was just l;ooking at my keyboard…yuk…it needs help!
Congrats on your winnings!! fun!


Accountant Big Bear Lake - Tax Services | B. Young & Associates Tax Service Inc.
No body looks forward to processing their tax returns. The entire process can be time consuming, confusing, and often times stressful. Ultimately, you just want to avoid owing any additional money to the IRS when you file taxes at the end of the year. If you happen to be lucky, you may even have a refund to look forward to in the end. Unfortunately, many people end up leaving hundreds of dollars in refund money on the table due to simple filing error. In fact, the amount of money that taxpayers fail to claim amounts to over a billion dollars.
For instance, Lots of people do not know that you may be able to deduct your state and local income taxes for your federal returns. If you live in a state like California that has high in-state income tax rates, you could be looking at a significant deduction. Other common deductions that are missed are student loan interest and medical expenses. You may be surprised how much your "small" deductions will add up to in the end. Your smartest bet is to let a tax professional handle your returns for you. Our team of knowledgeable associates will comb through all of your expenses throughout the year and help you get the most out of your itemized deductions.
It really pays to keep all of your records in great order during the year. Come tax time, you don't want to be looking high and low for significant receipts and documents. If you haven't done a great job of keeping your tax information together so far this year, it's not too early to start. A great way to get back on track is to pull your previous year's returns and look at the information you used to file those. That will help you create a thorough checklist of all the documents you'll need to track down before it's time to file your next returns.
Lots of of these companies have the option to receive online updates if forms or rules change before you submit your taxes, and their automated system will examine your return for errors prior to allowing you to file. However, even with these precautions in place, it's still possible for errors to occur on your return. Even if your software doesn't find any errors, you should still check your returns thoroughly before submitting them. You could make entry mistakes on your reported income, social security number or other personal information that the computer software has no way of catching. If such a mistake occurs on your taxes if could result in the IRS rejecting your return or holding up your refund.


A couple of months ago, Yahoo debuted a new messaging app called Squirrel and offered it as an invite only beta for anyone interested. Now the app has been released as Yahoo Together and is available for download on iOS and Android.
Yahoo Together replaces Yahoo Messenger, which was retired by the company earlier this year. In fact it comes from the same team behind Yahoo Messenger and uses your Yahoo account. You can invite people to your group who are not signed up by using a unique code that the invitee can enter upon signing in.
The interface is very similar to one of its competitors in the market, Slack. Essentially, Yahoo Together is a group messaging app that makes it easy to get organized and make plans with features like reminders, custom reactions and a mute function.
Topics — Keep your group conversations ultra-organized with topics.
Secret topics — Use secret topics like Mom's Birthday Surprise for private conversations.
Reminders — Make plans and don't flake out. Automatically set group reminders by tapping a message and hitting remind.
Custom reactions — Make inside jokes official. Use any image or selfie to design custom reactions.
Mute — Turn off notifications for topics that are a snore.
Blasts — Hit blast to make sure everyone in your group sees important messages.
Attachments — Share photos, documents or links. Easily find them later all in one place.
Activity view — Never miss an important message. Know when you are mentioned, all in one view.
Privacy — Invite your group with a link. No need to share your contacts with us.
While we'd like to see features like voice calling on Yahoo Together, for now it will have to make a name for itself with what it offers and hope it doesn't suffer the same fate as its predecessor. Will you be using Yahoo Together ?


'This week he worked Monday alone here with our coaches and also yesterday and today he's working with a different adaptation, better than last week. "I spoke with the players [and told them] we need to think this match is very important for us".
"Above all we must work hard, take a good feeling in training and then show it in the match".
His inconsistent performances and struggles with fitness this term are understood to have convinced Emery that letting him go in the next transfer window is the best option, though the Gunners will likely have to accept a reduced fee for the German global. We started very well away, changing our mentality to get more points.
According to the Macclesfield Town manager, Arsenal boss Unai Emery needs at least two to three transfer windows to turn things around at the club. After that, we know we can win. We've won with three and we've won with two.
'Away each match is a new challenge but it's also a very big opportunity to take the three points and continue in our way better than we're doing now away'. "We need to be confident and take more confidence and continue working". This week we've had good days of training because the feeling of the players and their wish to work every day is good. "If we can not, it's different".


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MUSIC NEWS: ZOAX Announce One-Off London Show At The Black Heart
If you're yet to see ZOAX in a live setting then now is definitely your time, as the band have announced a special one-off show at London's Black Heart. The gig will take place on the 23rd February ahead of the band's run on Funeral For A Friend's Farewell Tour.
The quartet have been working hard on their debut album, which is due for release in April – you can expect to hear some of the band's new material live at this show as well as favourites from their XIII and Is Everybody Listening? EPs.
Keep up to date with ZOAX via their Facebook page.
Tags : Black HeartcamdenFuneral for a FriendZoax
VIDEO NEWS: Press To MECO Reveal 'Diffusion Of Responsibility'
FESTIVAL NEWS: Roskilde Festival Confirms Frank Carter & The Rattlesnakes, Ghost And More
FESTIVAL REVIEW: Download 2022 – Saturday
VIDEO NEWS: Holding Absence Release Live Video For 'Drugs And Love'
MUSIC NEWS: Holding Absence Announced As Main Support To Funeral For A Friend On Upcoming UK Tour


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Energy drinks serving up excessive amounts of sugar and caffeine in one serve
By Lucy Cormack
October 24, 2016 — 4.21am
There are few people who would willingly tuck into a bowl filled with 21 teaspoons of sugar just before sitting an exam.
And yet teenagers and young people that throw back a standard 500mL energy drink are doing just that.
On the Australian market, sales of energy drinks have risen by an average of 6.7 per cent every year since 2010.
Just one 500mL can of Rockstar Punched Energy + Guava tropical guava flavour ($2.60 at Coles) contains 21 teaspoons or 83.5 grams of sugar, and 160 milligrams of caffeine.
One can of Rockstar Punched contains 21 teaspoons of sugar. Credit:Ryan Stuart
Coca-Cola Amatil's 500ml Mother ($2.80) contains 13 teaspoons of sugar and 160mg of caffeine, while 250mL cans of Red Bull ($2.85) and Mother ($2.86) serve up seven teaspoons of sugar and 80mg of caffeine
The high levels of caffeine have made such beverages a favourite among young people, particularly students preparing for their HSC exams.
Their popularity has prompted a coalition of 13 leading health and community organisations to issue a warning that about possible health risks.
"[Energy drinks] are a risky drink choice...especially for students who may be consuming several a day during this stressful end of year exam period," said Craig Sinclair, public health committee chair of the Cancer Council Australia.
What 21 teaspoons of sugar really looks like. Credit:Ryan Stuart
The organisation has joined Diabetes Australia, the Heart Foundation, Nutrition Australia and others for the Rethink Sugary Drink Campaign, which calls for a 20 per cent tax on sugary drinks, a public education campaign and tougher sale restrictions in schools and sports centres.
"If consumed regularly the high sugar content in energy drinks can lead to weight gain and obesity, increasing your risk of heart and kidney disease, type 2 diabetes, stroke and some cancer," Mr Sinclair said.
A 500ml can of Mother contains 13 teaspoons of sugar and 160mg of caffeine. Credit:Lucy Cormack
Dr Peter Alldritt, of the Australian Dental Association, said energy drinks also contributed heavily to "tooth decay and erosion."
As a teacher at a co-ed private school in Sydney last year, Emily* witnessed at least two students who developed "definite addictions" to energy drinks in their HSC year.
Health experts have called out marketing practices of brands like Red Bull for targeting young people. Credit:Lucy Cormack
"For one student it turned into a cycle where he was unable to sleep, so he was drinking more and more. Eventually he was drinking about six 250mL cans a day."
Emily said a second student, who was drinking up to three cans a day, was "helped to come off them," by another teacher, but doing so left him unable to work.
"It was a definite addiction for both students. They didn't know how to, or didn't want to stop."
The short-term effects of energy drinks include alertness, stimulation of the nervous system and an increased heart rate, while excessive consumption can cause insomnia, nausea, vomiting and heart palpitations.
In both 2014 and 2015 the NSW Poisons Information Centre hotline received more than 40 calls related to energy drinks.
Energy drink sales in Australia and New Zealand increased from 34.5 million litres in 2001 to 155.6 million litres in 2010, according to the Australian Bureau of Statistics.
However a spokesman for the Australian Beverages Council said, ABS data also confirmed energy drinks represented less than 0.4 per cent of total intake of all non-alcoholic, non-dairy beverages among 14 to 18-year-olds.
"In this demographic, just 1.7 per cent consumed energy drinks," he said, adding that Australia had "some of the toughest regulations in the world."
While the industry does not make drinks available in secondary schools, the Rethink Sugary Drink Campaign argues that heavy marketing tactics do target young people.
Mr Sinclair said major brands like Red Bull, Monster and Rockstar "pour enormous amounts of money into partnerships with activities young people enjoy," like extreme sports, music festivals, and Schoolies-related events.
A spokesperson for Frucor, the manufacturer of Rockstar, said labelling on its cans recommended no more than one can was consumed each day.
"Rockstar supports events aimed at consumers aged older than 18. We do not provide samples to anyone aged 18 or under."
Coca-Cola Amatil said Mother was not marketed to children and labelling on all cans recommended a maximum daily intake of 500mL.
"An older teen's decision to drink an energy drink is akin to deciding to have a cup of coffee. They are old enough to make that decision for themselves."
*Name changed to protect student privacy.
Latest consumer news
Lucy Cormack
Lucy Cormack is a crime reporter with The Sydney Morning Herald.
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Toy Story That Time Forgot (television) Christmas special on ABC, aired on December 2, 2014. During a post-Christmas play date, the Toy Story gang finds itself in uncharted territory when the coolest set of action figures ever turn out to be dangerously delusional. It is all up to Trixie, the triceratops, if the gang hopes to return to Bonnie's room. Directed by Steve Purcell. Voices include Tom Hanks (Woody), Tim Allen (Buzz Lightyear), Kristen Schaal (Trixie), Timothy Dalton (Mr. Pricklepants), Joan Cusack (Jessie), Wallace Shawn (Rex), Don Rickles (Mr. Potato Head). From Pixar Animation Studios.


Whilst sailing abeam of the Cape of Good Hope, at the gateway to the Indian Ocean at 48 degrees South, Thomas COVILLE has just been through one of the most stressful nights of his sailing life.
Thomas COVILLE's (FRA) attempt at the solo round the world record has been through a difficult few days. After a slow couple of days he's dropped over two days behind Francis JOYON's (FRA) pace, already he remains slightly ahead of Ellen MACARTHUR's (GBR) current record time.
Imagine Michael SCHUMACHER hurtling along at 300 km/hour in the pitch black, all his headlights turned off, at the wheel of his Formula 1, and added to that, on terrain closer to Paris-Dakar than a tarmac circuit. All that to explain that at the point where we in Europe were tucked up under our duvets, the skipper of Sodeb'O had got out his dry suit and his survival kit, his stomach in knots, his throat dry and his eyes stinging through scanning the radar intently. COVILLE spent the night at over 25 knots amidst the icebergs with two obsessions: keeping his nerve and remaining lucid so as not to end up astride of an iceberg, whilst making as fast a headway as possible in order to stay ahead of this depression, which is enabling him to progress on flat seas.
COVILLE described the experience in his latest communication: "At 48° 45 South and 10° 19 East, I am an eyewitness to this infamous global warming. As far as I can remember, I've never seen ice so far north during this season. These cathedrals of ice, these temple keepers which remain on the blue planet, adrift of the Minquiers, I don't know how to describe these great forms sculpted by the wind and the sea. Victor HUGO imagined them, I've actually seen these petrified tempests. I thought I'd got clear of them but the water temperature dropped off sharply at 5° then 4.9°, a sign of their proximity. Out on deck and the atmosphere is icy. The apparent wind, created by the boat speed, increases the chill factor. Dawn turns everything white. I've uncovered the contours of the boat. The white foam from the gusts breaking on the water could be mistaken for a sheet of ice. I catch myself a little more with each of them. Far away, a more limpid mass emerges, just to my east. I hold my breath, another one? This is but the first rays of daylight, which are just coming out from under the clouds on the horizon. I manage to find the strength to smile. I'm going to rediscover my eyes for a few hours. Last night was one of the longest in my existence. I'll have to ensure I sleep a little before the next one..."
At midday today, Sodeb'O was sailing 140 miles from the Cape of Good Hope, which it is set to round between 18:00 and 19:30 hours UTC this evening. COVILLE currently has a lead of over 775 miles on MACARTHUR's record on B&Q Castorama, that is over 2 days and 5 hours, and a 1,363 mile deficit on JOYON and the Trimaran IDEC. At the entrance to the Indian Ocean, COVILLE is likely to have conceded a little over 2 days and 16 hours to JOYON.
In the early morning, the winds had dropped off slightly as the trimaran was rounding to the south of a zone of high pressure. A new depression is set to propel them towards the Kerguelen Islands. Some 3,810 miles from the Cape of Good Hope, this second cape will mark the entry into the Pacific no man's land.


"I am forever grateful for hemtjänstpersonalen" "When my beloved father was about to go away so he wanted to die at home." "It was his last wish." "
11 Şubat 2019 Pazartesi 17:02 - 3 reads.
"I am forever grateful for hemtjänstpersonalen"
"When my beloved father was about to go away so he wanted to die at home."
"It was his last wish."
"It would put high demands not only on the us relatives, but also in home care."
"My father, who was dying of cancer could receive palliative care in the home. In addition to it he needed the help of home care."
"We kin did our best to take care of him as long as it went."
"But when his care needs became too great, associated home care."
"It would appear that he then had two months left to live."
"My father, who had strong integrity, opposed from the beginning home care services. He did not want "a lot of the spring" or "a lot of different people" in his home."
"But when the end inexorably approaching, the came home to get a crucial. The staff was quickly forced to put themselves into his care."
"I expressed a strong wish that the home would try to send the same people all the time and so get different as possible, so that he would be able to feel safe."
"And the more helpless my father became, the less was the circuit that came to care for him. Towards the end came only the most experienced to take care of my dad."
"That was how I experienced it."
"The municipal hemtjänstpersonalen came to perform a far outstanding work."
"It seemed to do its best to piece, so that the last time in my dad's life would be as good and as possible."
"Those who came were all deeply empathetic, knowledgeable and cared for my father gently."
"the Number of people that came was towards the end becoming fewer and fewer. I felt, therefore, that he had a coherent care."
"I can't imagine how his last days would have been if he had been forced to face 24 different faces, or even more. If it constantly had new people arrived who did not know his condition, his routines or his needs."
"When someone is approaching death it is important to be responsive, flexible, empathetic and gentle, because the patient's condition is changing rapidly and deteriorate."
"All this was the wonderful hemtjänstpersonalen be."
"It was, therefore, not only a great support for my dad, but also for me as a family member."
"These people succeeded with his compassion to give my dad a dignified end."
"For this I am them forever grateful."


Hello everyone, sorry this post is coming a bit late! I just thought that I'd give you a little update on my plans for this year on my blog, I'm not doing any 'new year's resolutions' or anything like that as to be honest it just isn't my thing. Instead I thought I'd focus more on the stuff I will actually be doing etc.
As you might have noticed I have really struggled to keep to my blogging schedule. I always plan to upload a new post on every Monday and Friday but this rarely actually happens! I think I was a bit better during my 12 Days of Blogmas but let's face it there have been a lot of gaps between posts in the last year. A couple of months saw no posts at all while the rest often involved a lot of me uploading posts a lot later than planned. Despite this 2015 has been one of my most successful years of blogging in terms of content, photography and you-know, actually blogging! I have been blogging on-off since I was at university but last year was the one where I actually stuck to it for more than a couple of weeks!
This year I've decided to take a slightly different approach. A lot of bloggers much more successful than I seemed to have found blogging motivation and the comparing themselves to other bloggers really hard and some of them have even reverted to just posting whenever they feel like it rather than stick to the schedules they imposed upon themselves. I fear that if I had no schedule I wouldn't ever blog at all and the idea of posting willy-nilly makes the frantic organiser in me a bit nervous. Instead I've decided to change both the day I post and the frequency that I post. I've no idea why I chose Monday's in the first place as I never do any blog preparation over the weekend so I've decided Wednesdays will be my ideal date and hopefully every other Friday too. I'm hoping that making things a little easier on myself will encourage me to stay on track as I'll be less likely to fall behind as quickly.
Next up I thought I'd talk content. Harry and I have decided to go invoke a spending ban throughout 2016 (eek!) but I'll be writing a full post on that soon and hopefully updating you throughout the year. That is one of the reasons why I haven't written a 'What I Got For Christmas' post, as instead I'll be using a lot of those products to write content for the coming months. I'm also hoping to get a lot more Disney themed posts on the blog. I did start a once a month series later on last year so I'll definitely be continuing that.
One of the things my blog has lacked sometimes is that personal touch. I have written the odd personal post but it is something that I find quite difficult to write. Despite that I often find writing about my experiences to be quite cathartic, so I hope to write more of those.
Finally although I did say no new year's resolutions, I will tell you what I hope for this coming year. I do hope to lose weight, I'm not making it a resolution as I've been losing weight for the past two years (I've written about my decision to start losing weight and about losing my first stone on this blog before) but I want to move more and make my body fitter and healthier in process. I also want to get better at blogging because it genuinely makes me feel happier and more motivated when I'm doing it! Lastly I'd like to get more involved in the blogging community, I did participate in a few twitter chats last year but then I fell out of the habit and my twitter has since been almost silent! I hope this post hasn't been too dull for you, I promise to make the rest of 2016 a bit more exciting!