text:
\section{Introduction}

The dispersion of phonons in metals has a `direct'
part, determined by the interactions between the ions,
and an indirect part determined by electron-phonon
coupling and the electronic polarisability \cite{phon}.
The damping similarly can arise from phonon-phonon
interaction - related to nonlinearities in the
inter-ionic potential, or the polarisability
- via particle-hole pair creation. Phonon physics
associated with ionic interactions is well
understood but the effects arising out of
a non trivial polarisability, in correlated
electron systems, have generated a new list of
questions.

Many electronic systems have now been shown
to exhibit behaviour that differs widely
from the band picture
\cite{dag}. In particular correlation
effects give rise to competing ordered phases,
short range order, and sometimes a pseudogapped
electronic spectrum - widely at variance with
band theory\cite{man,cup}. The short range order
gives a characteristic momentum dependence to
electronic properties, the pseudogap generates
a new frequency scale, and temperature plays
an important role in the evolution of both these
features.
The electronic polarisability $\Pi({\bf q},\Omega, T)$,
where ${\bf q}$ is the momentum, $\Omega$ the frequency,
and $T$ the temperature, becomes a non trivial function
- very distinct from its weak coupling Lindhard counterpart.
It is no wonder that phonons in these correlated systems
show a very rich behaviour.

For example, recent experiments
\cite{weber1,weber2,weber3} reveal
the impact of short-range
charge order (CO),  and an electronic pseudogap,
on the softening and broadening of the
bond stretching phonons in the manganites
for momenta near the
CE ordering wavevector.
Similar effects on phonons have
been observed in underdoped
cuprates\cite{reznik,dean},
possibly owing to stripe order.
In fact phonon properties near
${\bf q} \sim (\frac{1}{4},\frac{1}{4},0) $,
the CE ordering wavevector, in manganites
are very similar
to that in cuprates at
${\bf q} \sim (\frac{1}{4},0,0)$.
In the
nickelates\cite{kajimoto}, inelastic
neutron scattering reveals strong softening and
branch-splitting of longitudinal optical (LO) phonons.
Strong phonon renormalizations
have also been reported in doped bismuthates\cite{braden}
possibly due to their coupling to interplanar
charge fluctuations.

There are two distinct scenarios to consider when
approaching these problems.
(a)~Situations
where the electron correlations
arise from inter-electron interactions - and the phonons
are only weakly coupled to the electrons, and
(b)~where electron-phonon interaction is itself
responsible (if only in part) for features in the
electronic spectrum. Category (a), possibly appropriate
to the cuprates\cite{cup}, requires a solution of the
interacting electron problem and then use of the
resulting $\Pi({\bf q}, \Omega)$ to determine
the phonon self-energy. Category (b) requires an
``ab initio'' handling of lattice distortions,
and is pertinent to the manganites\cite{man}.

This paper
is focused on understanding phonons in a model
that approximates the manganites. We will consider
models in category (a) elsewhere.
To set the stage we quickly recapitulate the
electronic observations in the intermediate
coupling manganites, and the recent results
on phonon spectra.

The manganites A$_{1-x}$B$_x$MnO$_3$,
where A is trivalent and B is divalent,
involve $e_g$ electrons Hund's coupled to $t_{2g}$
based core spins, and to Jahn-Teller (JT) distortions
of the MnO$_6$ octahedra\cite{man,millis1}.
The Hund's coupling promotes ferromagnetism
(and extended electronic states) while the JT
coupling favours polaron formation (and electron
localisation). The bandwidth and carrier density
can be tuned via choice of the A and B ions, and
$x$.
A material that is a ferromagnetic metal (FM)
 at low
temperature can show polaronic signatures with
increasing temperature as spin randomness reduces
the effective bandwidth.
In fact it can cross over to a paramagnetic
insulator (PI) across the magnetic transition.
There is naturally a drastic change in the
electronic spectra with temperature in this
parameter window.

\begin{figure}[b]
\centerline{
\includegraphics[width=6cm,height=5.4cm]{1}
}
\caption{Phonon `phase diagram' for the 2D
        double exchange Holstein model near half filling
        for varying coupling and temperature.
        We normalize coupling $g_{H}$ by the zero temperature
        critical coupling for polaron formation
        $g_c$ and temperature by the ferromagnetic
        transition temperature at weak coupling
        $T^{0}_{c}=2\Omega_{0}$, where $\Omega_{0}$
        is the bare Holstein frequency.
        FM and PM denote
        the ferromagnetic and paramagnetic metal phases,
        similarly FI and PI are ferro and para insulating
        phases. The phonon regimes are indicated in blue.}
\end{figure}

Inelastic neutron scattering
has uncovered the following phonon features
in this regime.
\begin{enumerate}
\item The
Mn-O bond stretching phonons along the (110)
direction in the bilayer manganite
La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ soften and broaden
close to the CE ordering wavevector in the low
temperature ($\sim10$K) metallic phase\cite{weber1}.
\item
A similar effect is observed in the 3D compound
La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ for the transverse
acoustic phonons, on heating through the Curie
temperature $T_c\sim350$K \cite{weber2}.
\item
In the charge and orbital ordered bilayer
manganite LaSr$_{2}$Mn$_{2}$O$_{7}$, one sees
a reduction in broadening and softening of low-energy
acoustic phonons on cooling below $T_{CO} \sim225$K
\cite{weber3}.
\end{enumerate}

We wish to address these issues, by first solving the
appropriate electronic problem.
To retain the key qualitative features of manganite
physics, and also to access large spatial scales, we
study a two dimensional model of electrons Hund's
coupled to core spins and to lattice distortions via
a Holstein coupling.
We retain weak disorder in the model - to mimic the
effect of cation disorder in the doped materials.
This problem is solved via a Monte Carlo method in
real space, and the electronic polarisability that
emerges is used to compute the phonon spectra.

We list our main results below. In our
notation $g_H$ is the Holstein
coupling and $g_c$ its value
for the adiabatic polaron transition.
\begin{enumerate}
\item
At $g_{H} \ll g_c$
the ground state is a ferromagnetic metal
at low temperature, with dispersive phonons that show
a Kohn anomaly close to half filling. With increasing
temperature spin disorder and thermally induced lattice
distortions create a a mild electronic pseudogap, and
also  broaden the  phonons considerably.
\item
For $g_{H} \lesssim g_c$ the interplay of electron-phonon coupling
and disorder localises the phonons.
The phonon spectrum, as a result, is quite
incoherent. The electronic density of states features
a pseudogap. Thermal effects further accentuate
lifetimes.
\item
For $g_{H} \gtrsim g_c$ the ground state is a
ferromagnetic insulator.
The electronic spectrum is gapped
and phonon band is narrow, with
bandwidth limited lifetimes. This is related to
emergent short-range order in the background. On
heating past the ferromagnetic $T_c$, phonon lifetimes
pick up.
\end{enumerate}

Fig.1 summarizes our findings regarding thermodynamic
phases (indicated in red), electronic states (in black)
and phonon regimes (in blue).
It's discussed in detail later in context of the
thermal physics. In reporting the results, we first
focus on the ground state. The next section exhibits
our findings about the thermal physics. This is followed
by the discussion section, summarizing the results and
making a qualitative correspondence with experiments,
and a concluding section.

\section{Model and method}

We study the disordered Holstein-double exchange (d-HDE)
model, coupled to acoustic phonons on a two-dimensional
square lattice. The full problem has three parts-
(i)~the `d-HDE' part - electrons
coupled to optical phonons and `core' spins,
in a weakly disordered background,
(ii)~an acoustic phonon mode, and (iii)~`weak'
coupling between the acoustic
phonons and electrons. The total Hamiltonian is:
\begin{equation}
H_{tot}=H_{1}+H_{2}+H_{3}
\end{equation}
The Hamiltonian for the d-HDE part is-
\begin{eqnarray}
	H_{1} &=& \sum_{<ij>\sigma} t_{ij}c^{\dagger}_{i\sigma}c_{j\sigma}
	-J_{H}\sum_{i}\vec{S}_{i}.\vec{\sigma}_{i}
	+ \sum_{i}(\epsilon_{i}-\mu)n_{i} \cr
        && ~~-g_{H}\sum_{i}n_{i}x_{i}
         +\sum_{i}(\frac{p^2_{i}}{2M} + \frac{1}{2}Kx^2_{i})
\end{eqnarray}

Here, $t_{ij}$'s are the hopping amplitudes. We study a
nearest neighbour model
with $t=1$ for a nearly commensurate density, viz.
$n=0.40$.
$K$ and $M$ are the stiffness constant and mass, respectively,
of the optical phonons,
and $g$ is the electron-phonon coupling constant.
We set $K=1$. In this paper, we
report studies for $\Omega_0 = \sqrt{K/M} = 0.05$,
which is a reasonable value for real materials.
$\vec{S}_{i}$'s are `core spins', assumed
 to be large and classical.
$\epsilon_{i}$ is a quenched binary disorder with zero mean
and value $\pm \Delta$.
The chemical potential $\mu$ is varied to maintain
the electron density at the required value. We'll work in
the extreme Hund's coupling limit $J_{H}/t\rightarrow \infty$.
This effectively enslaves the electrons spins to the core spin
orientation and one obtains an effectively spinless, hopping
disordered model-
\begin{eqnarray}
H_{1}&=&\sum_{<ij>}t_{ij}{\gamma}^{\dagger}_{i}{\gamma}_{j}
+\sum_{i}(\frac{p^2_{i}}{2M} + \frac{1}{2}Kx^2_{i}) \nonumber \\
&+& \sum_{i}(\epsilon_{i}-\mu-g_{H}x_{i})n_{i}
\end{eqnarray}
The hopping amplitude depends on spin
orientation via the relation-
\begin{equation}
t_{ij}/t=cos\frac{\theta_i}{2}cos\frac{\theta_j}{2}
 + isin\frac{\theta_i}{2}sin\frac{\theta_j}{2}e^{i(\phi_i-\phi_j)}
\end{equation}
where the $\theta_i$ and $\phi_i$ are, respectively,
 the polar and azimuthal angles of the core spins $\vec{S}_{i}$.
The Hamiltonian for the bare acoustic phonons is-
\begin{equation}
H_{2}=\sum_{\vec{q}}\omega_{\vec{q}}a^{\dagger}_{\vec{q}}a_{\vec{q}}
\end{equation}
with the bare dispersion
given by the equation-
\begin{equation}
\omega^2_{\vec{q}}=\frac{2\kappa}{\mu}(2-cos(q_x)-cos(q_y))
\end{equation}
We choose $\kappa=1.0$ and $\mu=2500$ as
parameters. This ensures that the maximum
of the acoustic branch is comparable
to the bare optical
mode frequency at the zone boundary.

The coupling between the acoustic phonons
and electrons is the third part of the Hamiltonian-
\begin{equation}
H_{3}=ig_{ac}\sum_{\vec{k}\vec{q}}\frac{|\vec{q}|}{\sqrt{2\mu\omega_{q}}}
(a_{\vec{q}}-a^\dagger_{-\vec{q}})c^{\dagger}_{\vec{k}+\vec{q}}c_{\vec{k}}
\end{equation}
We've written the parts $H_{2}$ and $H_{3}$ in momentum
space for simplicity, but the actual calculations using
them have been implemented in real space. This has the
advantage of capturing spatial correlations amongst
static distortions and the
core spin angles at finite temperature.

We solve the problem hierarchically. First, the d-HDE
problem is tackled in the adiabatic regime (assuming
$\Omega_0/t  \rightarrow 0$).
The $H_{1}$ part in the model leads to the action
\begin{eqnarray}
S &= &\int_0^{\beta}d\tau[
\sum_{ij} \bar{\psi_i}
\{(\partial_{\tau}+\epsilon_i-\mu)\delta_{ij} - t_{ij} \} \psi_j
\cr
&&~~+ \sum_i\bar{\Phi}_i(\partial_{\tau}+\Omega_0) \Phi_i
-~ g_{H}\sqrt{\frac{\Omega_0}{2K}}
\sum_{i}(\bar {\Phi}_{i}+\Phi_{i}){\bar\psi_{i}}\psi_{i}]
\nonumber
\end{eqnarray}
Here $\psi_{i}$ and $\phi_{i}$ are the fermion
and coherent state Bose
fields respectively.
$\beta$ denotes the inverse
temperature, and we use units where
$k_{B}=1$, $\hbar=1$. The relation
between the real and coherent state fields is
\begin{equation}
x_{i}=\sqrt{\frac{1}{2M\Omega_0}}(\Phi_{i}+\bar{\Phi}_{i})
\end{equation}

In quantum Monte Carlo (QMC)
\cite{QMC}, one `integrates
out' the fermion fields
to construct the effective bosonic action. The
equilibrium configurations $\Phi_i(\tau)$
of that theory are obtained via
sampling.  Physical correlators are then
computed as averages with
respect to these $\Phi_i(\tau)$
configurations. Within DMFT
\cite{DMFT} one maps the
original action in Eq.(2) to an
impurity problem, with parameters determined
through a self-consistency condition.

In the
adiabatic limit, or using the static path
approximation (SPA) strategy,
one treats the $x_{i}$ as classical
fields, neglecting their imaginary
time dependence. This corresponds to
$M \rightarrow \infty$ for a fixed $K$. In addition, the $\theta_i$
and $\phi_i$ angles also fluctuate at finite
temperature. Our method retains the quantum character
of lattice vibrations perturbatively.

The full action containing the electrons,
displacement fields and core spins can be
rewritten in frequency space as-
\begin{eqnarray}
S &=
&S_{ph} + S_{f}\nonumber \cr
S_{ph}&=&\frac{1}{2}\sum_{i,m}\bar x_{im}(M\omega_{m}^{2}+K)x_{im} \cr
S_{f} &=&\sum_{i,j,\alpha,\beta}\bar{\psi}_{i\alpha}
[(-i\omega_{\alpha}+\epsilon_i-\mu)\delta_{ij}\delta_{\alpha\beta}
- t_{ij}\delta_{\alpha\beta}  \cr
&&~~~~~~~~~~~~~~~~~~-g_{H}\sqrt{\beta}x_{i,\alpha-
	\beta}\delta_{ij}]\psi_{j\beta}
\end{eqnarray}
where $\alpha$ and $\beta$ are fermionic
 Matsubara frequencies, $m$ is
a Bose frequency. To get the partition function,
one integrates over $\psi_{i\alpha}$, $x_{i0}$ and the
$x_{im}$ fields and of course,
the angular variables hidden in $t_{ij}$.

The next step is to separate the Bose
field into zero
and non-zero Matsubara modes.
We write $S=S_0 + S_1$ where
the first part contains fermions
 coupling only to the
zero frequency (static) mode and
 the second, the finite modes.
We can formally `diagonalize' the
 fermions in presence of the
static mode to write $S_0$ as-
\begin{equation}
S_{0}={\sum_{l,\alpha}\bar{\xi}_{l,\alpha}
	(-i\omega_{\alpha}+\epsilon_l)\xi_{l,\alpha}} +
\frac{1}{2}K\sum_ix^2_{i0}
\end{equation}
where $\xi$'s correspond to
the fermionic eigenmodes in the
$\{x_{i0} ,\theta_i,\phi_i\}$ background.
$S_0$ defines the static path
approximation (SPA) action.

The eigenvalues ($\epsilon_l$'s )
depend  non-trivially on the
$\{x_{i0} ,\theta_i,\phi_i\}$ background.
To obtain the effective zero mode
distribution $P\{x_{i0},\theta_i,\phi_i\}$,
one has to integrate out the
fermions. At the SPA level,
 there exists an effective
Hamiltonian $H_{eff}$,
depending on $\{x_{i0},\theta_i,\phi_i\}$,
for the fermions and the
distribution can be formally written as-
\begin{eqnarray}
H_{eff} & =& \sum_{<ij>}t_{ij}
{\gamma}^{\dagger}_{i}{\gamma}_{j} -
 g \sum_{i}n_i x_{i0} \cr
P\{x_{i0},\theta_i,\phi_i\} &= &
Tr_{{\gamma},{\gamma}^{\dagger}}e^{-\beta (H_{eff} +
	{1 \over 2} K x_{i0}^2) }
\nonumber
\end{eqnarray}

Around the SPA action, we set up a
 cumulant expansion of $S_1$.
Owing to the disparate timescales of the
 optical phonons and electrons,
we attempt a sequential integrating out. First,
the fermions are traced out and one obtains
the following expression for $S_1$
in terms of the $x_i(i\Omega_m)$:
\begin{eqnarray}
S_1 &=
&S^{\prime}_{ph}-Trln[\beta
((-i\omega_{\alpha}+\epsilon_i-\mu)\delta_{ij}\delta_{\alpha\beta} \nonumber
\\  &&~~~~~~~~~~~~~~~ -t_{ij}\delta_{\alpha\beta}-g_{H}\sqrt{\beta}x_{i,\alpha-
	\beta}\delta_{ij})]\nonumber\\
S^{\prime}_{ph}&=&\frac{1}{2}\sum_{i,m\neq 0}\bar
x_{im}(M\omega_{m}^{2}+K)x_{im}
\end{eqnarray}

\begin{figure*}[t]
\centerline{
\includegraphics[height=6cm,width=16cm]{2a}
}
\vspace{.5cm}
\centerline{
\includegraphics[height=4.5cm,width=5.3cm]{2b}
\includegraphics[height=4.5cm,width=5.3cm]{2c}
\includegraphics[height=4.5cm,width=5.3cm]{2d}
}
\caption{Top row: Snapshots of static optical phonon
        backgrounds in the ground state for weak ($g/g_c=0.8$,
        left panel), intermediate ($g/g_c=1.0$, middle panel)
         strong ($g/g_c=1.2$, right panel) couplings. We see a
          gradually developing short-range ($\pi,\pi$)
          correlation on moving from left to right, bottom
          row: a) left panel- Distribution of static distortions
          $P(x)$ for three couplings.
We see a weak bimodality transforming to a prominent two-peak distribution at
          strong coupling, b) middle panel- static phonon
          structure factor along the BZ diagonal $S(q,q)$
          for the same coupings, confirming features seen
          in lattice backgrounds, c) right panel-
          electronic density of states $N(\omega)$ from
          weak to strong coupling. We see an evolution from
          tight-binding like spectrum to a small hard-gap DoS
          at strong coupling through a pseudogap regime.
}
\end{figure*}

Analytic determination of the trace is impossible beyond
weak coupling.
Our method constitutes of
expanding the trace in finite
 frequency $x_{i}$ modes upto Gaussian
level. Physically, we assume
 that the quantum fluctuations are small
in amplitude, controlled by a
 low $\gamma=\Omega_0/t$ ratio.
Retaining only
quadratic terms in the dynamic
 modes allows us to analytically
integrate them out later.
An analogous strategy
 has been explored within DMFT before\cite{millis2}.

 The method is obviously perturbative in $\gamma$
 as we diagonalize the fermions
 in presence of static
distortions and evaluate
correlation functions on this `frozen'
background, which enter
 as coefficients of the
 quadratic Bose term
for finite frequencies. After
re-exponentiating this term
(in the Gaussian
approximation spirit), the new partition
function becomes-
\begin{equation}
Z = \int [D\bar{x}][Dx][D\theta]
[D\phi][D\bar{\xi}][D\xi]e^{-(S_{0}+S_{1})}
\end{equation}
where
\begin{eqnarray}
S_{0}&=&{\sum_{l,\alpha}\bar{\xi}_{l,\alpha}
	(-i\omega_{\alpha}+\epsilon_l)\xi_{l,\alpha}}
	+\frac{1}{2}Kx_{i0}^2\\ \nonumber
S_{1}&=&{\sum_{i,j,m>0}\bar{x}_{im}[(M\omega^2_{m}
	+K)\delta_{ij}+{g_{H}^2}
	\Pi_{ij}^{m}(\{x_{i,0},\theta_i,\phi_i\})]x_{jm}}\\ \nonumber
\end{eqnarray}

$\Pi_{ij}^{m}$ is a one-loop
 fermion polarization correcting the
free Bose propagators. The expression for this is
\begin{equation}
\Pi_{ij}^{m}(\{x_{i0},\theta_i,\phi_i\})=
\frac{1}{\beta}\sum_{\alpha}G_{ij}^{m}G_{ji}^{\alpha-m}
\end{equation}
$G_{ij}^{m}$'s are Matsubara components
 of real-space fermion Green's
functions computed in an arbitrary static
 background. One can write a spectral
representation of this as follows-
\begin{equation}
G^m_{ij}(\{x_{i0},\theta_i,\phi_i\})=
\sum_n \frac{u_{in}\bar{u}_{jn}}{i\omega_m-\epsilon_n}
\end{equation}
where $u_{in}$ is amplitude at site $i$ for the
$n$th eigenstate of
the SPA Hamiltonian and $\epsilon_n$'s are
the corresponding eigenvalues.

\begin{figure*}[t]
        \centerline{
                \includegraphics[width=16cm,height=9cm]{3}
        }
        \caption{ Spectral distribution of the optical (top panel)
                and acoustic (bottom panel)
                phonon Green's function for varying
                $g_{H}$ in the ground state. The trajectory
                chosen along BZ is $(0,0)\rightarrow(\pi,0)\rightarrow(\pi,\pi)\rightarrow
                (0,0)$. Coupling increases along the horizontal axis in the following sequence
                (from left to right)- $g_{H}/g_{c}=(0.81, 1.00, 1.25)$.
                The critical coupling at this density is $g_{c}=1.60$.
                For the acoustic plots, $g_{ac}=g_{H}$.}
\end{figure*}

If we integrate out the finite
frequency Bose modes (in $S_1$),
a new $x_{i0}$ theory emerges.
One can treat this
resulting action with classical Monte Carlo (MC)
simulations to obtain the
optimal background in which the fermions move.
This basically means
that at each MC update, one uses the sum of the
SPA free energy and
the contribution from the finite frequency
Gaussian fluctuation,
to compute the update probability.

The coefficient of the quadratic Bose
term of $S_1$ in (13) defines the inverse
propagator $(D^{-1})_{ij,m}$ for the
 renormalized optical phonons. One can
  view the $\Pi^{m}_{ij}$ as a self-energy
  for the phonons in real space,
  correcting the bare propagator. To
get the renormalized Green's function,
one needs to solve a Dyson's equation
on the lattice with possibly inhomogeneous backgrounds.
\begin{equation}
[D]^{-1}_{ij}(\omega)=
[D]^{-1}_{0,ij}(\omega)+g_{H}^{2}[\Pi]_{ij}(\omega)
\end{equation}
Here the bare phonon
 propagator $D^{-1}_{0,ij}$ is defined
through the equation-
\begin{equation}
[D]^{-1}_{0,ij}(\omega)=(M\omega^2-K)\delta_{ij}
\end{equation}
where we have analytically
continued the Green's functions to real
frequency and $D^{-1}_{0,ij}$
denotes the inverse propagator for
the bare phonon.
This involves
a calculation that grows as $O(N^4)$
with increasing lattice size $N$. For
lattices of size 24$\times$24, this
computation was implemented.

Next, we consider the acoustic phonons.
As commented earlier, we rewrite the parts
$H_{2}$ and $H_{3}$ in real space-
\begin{eqnarray}
H_{2}&=&\sum_{ij}M_{ij}a^{\dagger}_ia_j \nonumber \\
H_{3}&=&\sum_{ij\vec{q}}
\frac{ig_{ac}|\vec{q}|}{\sqrt{2\mu\omega_{\vec{q}}}}
(a_je^{i(\vec{r}_i-\vec{r}_j).\vec{q}}-h.c.)c^{\dagger}_ic_i
\end{eqnarray}

The bare phonon is found
by just inverting the
matrix $M_{ij}$ in $H_{2}$.
 Its explicit form is given by-
\begin{equation}
[\tilde{D}]_{0,ij}(\omega)=\frac{e^{-i(\vec{r}_i-\vec{r}_j).
\vec{q}}}{\omega-\omega_{\vec{q}}+i\eta}-
\frac{e^{-i(\vec{r}_i-\vec{r}_j).\vec{q}}}
{\omega+\omega_{\vec{q}}-i\eta}
\end{equation}
where $\eta$ is a positive infinitesimal.
The coupling $H_{3}$ gives a self-energy
contribution, which can be
written as a matrix product-

\begin{figure}[b]
\centerline{
\includegraphics[height=8cm,width=8.5cm]{4}
}
\caption{Momentum resolved spectral functions
        $A(\pi,0)$ and $A(\pi,\pi)$ (left and right panels) of
        the optical (top row) and acoustic (bottom row) phonons
        for varying $g_{H}/g_c=(0.8,1.0,1.2)$. The relevant
        couplings along with color codes are
        listed. }
\end{figure}
\begin{figure}[t]
\centerline{
\includegraphics[height=3.5cm,width=8.5cm]{5a}
}
\centerline{
\includegraphics[height=3.5cm,width=8.5cm]{5b}
}
\caption{Fitting of optical (top panel) and acoustic (bottom
        panel) phonon spectra for the ground state in terms of
        mean frequencies
($\bar{\omega}(\vec{k})$ and linewidths ($\Gamma(\vec{k})$
        throughout the BZ trajectory
$(0,0)\rightarrow(\pi,0)\rightarrow(\pi,\pi)\rightarrow
        (0,0)$. The relevant couplings are listed along with
        color codes.}
\end{figure}

\begin{equation}
\tilde{\Pi}_{ab}={A}_{ai} {\Pi}_{ij} {B}_{jb}
\end{equation}
where $\Pi_{ij}$ is the same
 as in equation (14). The matrices
sandwiched to the left and
right are comprised of weighted
 form factors. They have
  the following expressions-
\begin{eqnarray}
A_{ai}&=&\sum_{\vec{q}}\frac{|\vec{q}|}{\sqrt{2\mu
\omega_{\vec{q}}}}e^{i(\vec{r}_i-\vec{r}_a).\vec{q}} \nonumber \\
B_{jb}&=&\sum_{\vec{{q}^{\prime}}}
\frac{|\vec{{q}^{\prime}|}}{\sqrt{2\mu
\omega_{\vec{{q}^{\prime}}}}}e^{i(\vec{r}_j-\vec{r}_b).\vec{{q}^{\prime}}}
\end{eqnarray}
Finally, a Dyson equation
is solved (in real space)
as in the optical phonon case-
\begin{equation}
[\tilde{D}]^{-1}_{ab}(\omega)=
[\tilde{D}]^{-1}_{0,ab}(\omega)-\tilde{\Pi}_{ab}(\omega)
\end{equation}

\section{Results on the ground state}

We organize the results as follows. First, the optimal static
background features are shown. These include
individual MC snapshots, the distribution of static
optical phonon distortions $P(x_{0})$
the static phonon structure factor along the BZ diagonal
($S(q,q)$) and electronic density of states (DoS) in the
ground state.
Next, the spectral maps in
($\vec{k},\omega$) space of the optical and acoustic
phonon propagators,
calculated with the full frequency dependent
$\Pi_{ij}(\omega)$, are featured. These spectra
were calculated for moderately large sizes (24$\times$24).
To enable a closer look into phonon properties, we plot the
lineshapes for a couple of high symmetry $k$-points in the BZ -
($\pi,0$) and ($\pi,\pi$).

\begin{figure}[b]
\centerline{
\includegraphics[height=3.5cm,width=4.0cm]{6a}
\includegraphics[height=3.5cm,width=4.0cm]{6b}
}
\centerline{
\includegraphics[height=3.5cm,width=4.0cm]{6c}
\includegraphics[height=3.5cm,width=4.0cm]{6d}
}
\caption{Ferromagnetic structure factor $S(0,0)$
	(top left) for three couplings of interest
	and static phonon structure factors $S(q,q)$
	along the diagonal of BZ for three temperatures
	$T/\Omega=(1.0,2.0,3.0)$ in subsequent panels.}
\end{figure}
\begin{figure*}[t]
\centerline{
\includegraphics[height=4cm,width=14.5cm]{7a}
}
\centerline{
\includegraphics[height=4cm,width=14.5cm]{7b}
}
\caption{Top row: The distribution of static optical mode
 distortions ($P(x)$) across three coupling windows
 a) weak ($g_{H}/g_c=0.8$), b) intermediate ($g_{H}/g_c=1.0$)
        and c) strong ($g_{H}/g_c=1.2$). The weak
        bimodality in the ground state at weak coupling
        smoothens out due to thermal
        fluctuations. At intermediate coupling, bimodality remains
        upto mild heating ($T/\Omega_0 \sim 1.0$). The strong
        coupling distribution is bimodal even upto
        $T/\Omega_0=3.0$. Bottom row: electronic DoS across the
        same couplings- d) a mild pseudogap seen at weak coupling
        for high $T$, e) intermediate coupling
        features gradually diminishing pseudogaps on heating,
        f) strong coupling DoS is gapped at
low $T$, has more robust pseudogap feature on heating.}
\end{figure*}

Given that it's difficult to interpret
these lineshapes directly, we've extracted mean
 frequencies and widths for the entire optical and acoustic
 phonon spectra. We also attempt to make a connection between
 the observed phonon features and the
corresponding electronic physics on the static backgrounds.
 The quantity which affects phonon features
 directly in our theory is the polarization
   $\Pi_{ij}(\omega)$. We don't provide any analysis
   of these in the present paper, but interpreting
   them is currently in progress.

\subsection{Backgrounds}

In this part, we show quantities characterizing the
static optical mode which controls most of the
phonon physics. First, the actual MC snapshots
of lattice distortions are featured, followed by probability
distribution of these ($P(x)$), which indicate polaron
formation. Next, the
structure factor along the BZ diagonal shows emergence
of short-range correlations near ($\pi,\pi$). Finally,
the electronic DoS in
 the ground state are exhibited, that
  show a gap formation at strong coupling.

The MC snapshots, shown in top row of Fig.2, reveal
static phonon correlations across various
coupling windows. These pictures are representative
of the ground state ($T/\Omega_0=0.2$). One sees a
 gradual improvement of $(\pi,\pi)$ correlations
 amongst the distortions as we move from weak
  to strong coupling (left to right). However, at
  weaker $g_{H}/g_c$, the features are much less underlined.
  In the clean Holstein model, the strong coupling
  state is supposed to be ordered, at least close to
   half-filling. Here, the weak binary disorder has
    the effect of destroying that, but short range
    correlations persist. The temperature scale for
    killing off these effects is set by $T_{CO}\sim\frac{t^2}{E_p}$.

\begin{figure*}[t]
\centerline{
\includegraphics[height=11.0cm,width=9.50cm]{8a}
\includegraphics[height=11.0cm,width=10.5cm]{8b}
}
\caption{Left set: Spectral distribution of the optical
phonon Green's function for varying
$g_{H}$ and temperature. The trajectory
chosen along BZ is $(0,0)
\rightarrow(\pi,0)\rightarrow(\pi,\pi)\rightarrow
(0,0)$. Coupling increases along the
horizontal axis in the following sequence
(from left to right)- $g_{H}/g_{c}=(0.81, 1.00, 1.25)$.
Temperature varies form top to bottom-
$T/\Omega_0=(0.6,1.0,3.0)$.
The critical coupling at this density is $g_{c}=1.60$.
Right set:
Spectral distribution of the acoustic
                phonon Green's function for varying
                $g_{H}$ and temperature. The trajectory
                chosen along BZ is $(0,0)
                \rightarrow(\pi,0)\rightarrow(\pi,\pi)\rightarrow
                (0,0)$. Coupling increases along the
                horizontal axis in the following sequence
                (from left to right)- $g_{H}/g_{c}=(0.81, 1.00, 1.25)$.
                Temperature varies form top to bottom-
                $T/\Omega_0=(0.6,1.0,3.0)$.
                The critical coupling at this density is $g_{c}=1.60$.
                For these plots, $g_{ac}=g_{H}$.
}
\end{figure*}

     The bottom row of Fig.2 shows first the distribution
     of static distortions. At the weakest coupling,
     a hint of bimodality is seen amidst a generally
     broad picture.
     On going closer to the actual crossover ($g_{H}/g_c=1.0$),
     a genuine two-peak distibution emerges with more
     weight on the smaller $x$ value. At strong coupling,
     a clear gap separates the two modes. The effect of
     disorder is to enhance polaronic features at
     weaker couplings and broaden the peaks
     at strong coupling.

     Next, we come to
     static phonon structure factor $S(q,q)$ in
      the ground state, from which the conclusions drawn
       from individual configurations can be further
       corroborated. Close to the zone boundary, we see mild
       peaks, whose weights become prominent at strong
       coupling.

      Finally, the electronic DoS also responds to the polaronic
      transition directly. We have a tight-binding like
      spectrum at weak coupling. The phonon induced
      renormalizations are small. Close to the transition,
      the behaviour changes qualitatively and a pseudogap
      emerges. At even higher couplings, polarons tend to order.
      As a result, we see formation of a small, hard gap.

\subsection{Overview of phonon modes}

In Fig.3, we exhibit the spectral maps of the optical
and acoustic phonons in various coupling regimes.
We already depicted such maps in our previous
work$\cite{sauri}$ on the clean Holstein model. The
 first row is depicting optical phonons on the ground
 state. Below $g_{H}=g_c$, the mode
 is fairly sharp except in the vicinity of $(\pi,0)$,
 and most noticeably
 around $(\pi,\pi)$, where it also splits and softens to
 some degree. We ascribe this behaviour to the proximity
 to a nesting instability ($n=0.4$ is close to half-filling).
 Compared to the clean Holstein problem,
the broadenings are considerably large in the present case. The reason is the
 presence of weak binary disorder, which also affects the
 Kohn anomaly like softening feature (near ($\pi,\pi$)) markedly.

\begin{figure}[b]
\centerline{
\includegraphics[height=7cm,width=8.5cm]{9}
}
\caption{Lineshapes of optical (top panel) and acoustic
        (bottom panel) phonons at $(\pi,0)$ and $(\pi,\pi)$
        for intermediate coupling ($g_{H}/g_c=1.0$).
        The relevant temperatures along with color codes
        are listed.}
\end{figure}
\begin{figure}[t]
        \centerline{
                \includegraphics[height=9cm,width=8.5cm]{10}
        }
        \caption{Fitting of optical phonon spectra at finite
                temperature in terms of
                mean frequencies ($\bar{\omega}(\vec{k})$) and
                linewidths ($\Gamma(\vec{k})$)
                throughout the BZ trajectory
$(0,0)\rightarrow(\pi,0)\rightarrow(\pi,\pi)
                \rightarrow(0,0)$. Each panel contains three
                temperatures- $T/\Omega_0=(0.6,1.0,3.0)$.
                Coupling increases
                from top to bottom in the following sequence-
                $g_{H}/g_c=(0.8,1.0,1.2)$.}
\end{figure}

 At $g_{H}=g_c$, polarons appear and
 the optical phonon spectrum becomes significantly
  broad due to presence of quasi-localized phonons.
  Except modes near the zone center ($0,0$), where
   scattering is prohibited owing to phase space
   constraints, a dramatic damping effect is seen. The
   softening is much less compared to the clean problem.

   Beyond the polaronic transition ($g_{H}/g_c=1.25$),
  the phonon branch sharpens again and the softening
   is considerably less. We see a remnant of the branching
  feature, observed prominently for the clean problem
  over a region in momentum space (from $X$ to $K$), owing
          to charge correlations and the resulting imperfect order.

 Moving to the second row, we discuss the acoustic phonon
  features now. Below $g_{H}=g_c$, the mode is clearly
  dispersive except around $(\pi,\pi)$, where it softens
  remarkably. We relate this feature, as in the
case of optical phonons, to the proximity to a nesting instability
  ($n=0.4$ in our study). We note that acoustic phonons
  respond to nesting physics much more dramatically, despite
  disorder effects being present.

  At $g_{H}=g_c$, polarons formation causes the phonon
  distribution to become significantly broad
due to formation of large static distortions.
Except modes near the zone center ($0,0$), where
scattering is prohibited owing to the form of
acoustic phonon-conduction electron coupling, a dramatic
  softening and damping is seen.

  Beyond the polaronic
  transition ($g_{H}/g_c=1.25$), the phonon branch sharpens
  again and the softening is considerably reduced.
  States near the Fermi level are depleted in this regime
  and hence the scattering is less.

\subsection{Detailed behaviour of phonon modes}

\subsubsection{Optical phonons}

The optical phonon lineshapes in the ground state (top
row of Fig.4) suggest that at $(\pi,0)$, we have a well-defined
mode at weak coupling ($g_{H}/g_c=0.8$). The spectrum evolves
to one having a long tail
towards lower frequencies close to the crossover. But,
on going further in the polaronic phase, the mode sharpens
once again, with a mild, split-peak feature.

The right panel in the top row exhibits the $(\pi,\pi)$
lineshape. This is broad even at weak coupling, with more
weight in lower frequencies. We ascribe this behaviour to
presence of disorder and proximity to perfect nesting, as
discussed earlier. On moving close to the crossover
($g_{H}/g_c=1.0$), the decoherence is more severe. Large static
distortions are deemed responsible for this. The spectrum
sharpens and hardens at strong coupling ($g_{H}/g_c=1.2$).
There's a hint of spectral splitting as well.

\begin{figure}[b]
        \centerline{
                \includegraphics[height=9cm,width=8.5cm]{11}
        }
        \caption{Fitting of acoustic phonon spectra at finite
                temperature in terms of
                mean frequencies ($\bar{\omega}(\vec{k})$) and
                linewidths ($\Gamma(\vec{k})$)
                throughout the BZ trajectory $(0,0)\rightarrow(\pi,0)\rightarrow(\pi,\pi)
                \rightarrow(0,0)$. Each panel contains three
                temperatures- $T/\Omega_0=(0.6,1.0,3.0)$.
                Coupling increases
                from top to bottom in the following sequence-
                $g_{H}/g_c=(0.8,1.0,1.2)$.}
\end{figure}

To gain further insight into the phonon features across
the full Brillouin zone, we've extracted mean frequencies
and linewidths along the BZ trajectory mentioned in the
maps. These are provided in the top row of Fig.5.
The softening (left panel) is clearly dominant at $(\pi,\pi)$,
and decreases at strong coupling. The linewdiths also
feature a peak at the same momentum point. The signature is
most prominent at intermediate coupling, when polarons start
forming but short-range correlations are still nascent.

\subsubsection{Acoustic phonons}

The acoustic phonon lineshapes on the ground state (bottom
row of Fig.4) show qualitatively similar trends
to the corresponding optical phonons at $(\pi,0)$
(left panel). One notable
difference lies in the fact that the mode softens instead
of hardening at intermediate coupling ($g_{H}/g_c=1.0$).
In the deep polaronic phase, the spectrum shifts again
to higher frequencies and lifetime is bandwidth limited.

The $(\pi,\pi)$ lineshapes (right panel) are more non-trivial
to interpret. The weak coupling spectrum has a mode at
very low ($\omega/t=0.01$) frequency. This is connected
to Kohn anomaly. Additionally, a broad shoulder is observed,
owing to disorder effects. The coherence at low frequency
is lost out closer to the transition, where the static
optical mode has large distortions. Going to higher coupling
($g_{H}/g_c=1.2$), the mode is still broad but regains
sharp features near the bare frequency. A splitting
character is observed similar to optical phonons.

In the bottom row of Fig.5, we plot the mean frequencies
and widths, as in case of optical modes. The undamped
Goldstone mode at $(0,0)$ is omitted for clarity. The sharp
dip of mean values near $(\pi,\pi)$ is underlined (left
panel). Corresponding linewidths, interpreted as lifetimes,
increase markedly near the transition ($g_{H}/g_c=1.0$).
We relate this to emerging short-range correlations amongst
polarons. Once the ordering sets in at strong coupling
($g/g_c=1.2$), widths decrease again.

\section{Effect of thermal fluctuations}

After discussing phonon properties for the ground
state and relating them
to background and electronic features, we now move
to the thermal physics. Fig.1 depicts the thermal
phase diagram in our model for high ($n\sim0.4$)
denisties. The FM and PM are ferromagnetic and
paramagnetic metallic phases. The corresponding
insulating phases are FI and PI, respectively.
The blue-lettered regions are phonon regimes.
In the weak coupling regime, standard
perturbation theory results for phonons are
useful. In the fan-like crossover region, phonons
are very broad ($\Gamma\sim\Omega_{0}$). Towards the
right, we have narrow band optical phonons. Compared
to the clean Holstein phase diagram\cite{sauri},
we see the region featuring electronic pseudogap
and `crossover' phonons have shifted to the left.
The electronic phases are indicated in black letters.

\subsection{Backgrounds}

The ground state of our model is ferromagnetically ordered
at all coupling windows, owing to double exchange interaction.
We first plot the $S(0,0)$ structure factor to infer
$T_c$ scales (top left panel of Fig. 6).
At weak coupling $g_{H}/g_c=0.8$,
the $T_c\sim0.07t$. This value reduces to $T_c\sim0.04t$
at strong coupling ($g/g_c=1.2$). The ferromangetic $T_c$
plays an important role in the broadening of phonons
as the interplay of spin disorder and thermal fluctuations
has direct impact on the electronic spectrum. This in turn
feeds back to the phonons through the polarization
$\Pi_{ij}(\omega)$ within our calculation.

The top right and bottom (left and right) panels of
Fig.6 show static phonon structure factors
(shown for the ground state in
Fig.2, middle panel) at finite temperature. The rising
feature near ($\pi,\pi$) survives and in fact grows
mildly on heating at weak coupling.

In Fig.7, the first row depicts static distributions of
optical mode distortions in various coupling regimes. The
left panel features weak coupling regime, where the
hint of bimodality observed in the ground state is wiped
out on mild heating. Increasing the temperature further
(going beyond ferro $T_c\sim0.07t$), we see a very broad
distribution skewed to lower $x$ values. The intermediate
coupling (middle panel) picture retains bimodality upto
the bare phonon scale $T/\Omega_0=1.0$. At strong coupling,
even at high $T$, we have a two-peak feature.

In the bottom row (Fig.7), thermal dependence of electronic
DoS is shown. The most non-trivial feature is a weak hint of
pseudogap at weak coupling (left panel). This arises out
of spin disorder, causing effective electron hopping to
weaken. There are also large thermal fluctuations of
the static mode, which grow into actual distortions
at intermediate coupling ($g_{H}/g_c=1.0$). There's a
pseudogap surviving upto high temperature in the middle
panel (close to crossover). At higher coupling (right panel),
the lowest $T$ features a small gap, that develops into
a robust pseudogap on heating up.

\subsection{Overview of phonon modes}

\subsubsection*{Optical phonons}

In Fig.8 (left set), we observe the spectral maps of
 the optical (left) and acoustic (right) phonons
 in various coupling
  and temperature regimes. The first row
  is representative of phonons at low $T$
  ($T/\Omega_0=0.6$). Ferromagnetic
  order is still present in the background.
  Below $g_{H}=g_c$, the
   mode is still `dispersive' except around $(\pi,\pi)$,
   where the softening feature is retained. At $g_{H}=g_c$,
   we now have thermal fluctuations of
       large static distortions playing out
       in tandem with magnetic fluctuations.
       Except modes near the
       zone center ($0,0$), a
       dramatic softening and damping is seen.
       The high temperature phonons are very broad ($\Gamma\sim
\Omega$).
       Beyond the polaronic transition ($g_{H}/g_c=1.25$),
        the phonon branch sharpens again and the softening
         is considerably reduced. The mild branching
         feature observed near ($\pi,\pi$) for the ground state
         is washed out. The role of disorder
         is to effectively promote electronic spectral
         gaps. Consequently, these phonons are less
         broad compared to those in the clean Holstein model.

\subsubsection*{Acoustic phonons}

Moving to the spectral maps of the finite temperature
acoustic phonons (Fig.8, right set), at the scale
of bare Holstein frequency ($T/\Omega_0=1.0$), we observe
quantitative changes at weak and
strong coupling but a significant increase in lifetimes
for the middle (intermediate coupling) picture. At even
higher temperatures, well past the ferro $T_c$
scale for all couplings, phonons in the polaronic side are rendered
quite broad and incoherent, except at low wavevectors.
The metallic side ($g_{H}/g_c\sim0.8$) is affected mostly
near $(\pi,\pi)$, where the degree of softening reduces
and lifetime picks up.

\subsection{Detailed behaviour of phonon modes}

As in case of the ground state, we study the phonons more
closely by examining specific lineshapes and fitting the
full spectrum to find mean frequencies and linewidths.
Here, we focus on the most interesting regime of
intermediate coupling ($g_{H}/g_c=1.0$).

\subsubsection*{Optical phonons}

In this regime, the polaronic crossover
causes both the ($\pi,0$) and ($\pi,\pi$) lineshapes
to have long tails at all temperature windows, as seen in
Fig.9 (top panel). The effect of large static distortions
is most prominent in the ($\pi,\pi$) lineshapes. Some features
of sharp peaks remain at low $T$, owing to limited
system size ($24\times24$) which gradually smudge out,
giving an incoherent spectrum with some weight near
the unrenormalized frequency on further heating
($T/\Omega_0=3.0$). One may ascribe this behaviour partly
to loss of ferromagnetic order also, which takes place
around $T=0.06t$.

Fig.10 shows the mean frequencies (left column) and
linewidths (right column) as functions of temperature
for three regimes. The
trends mentioned previously are clealy visible. First,
at `weak' coupling, proximity to a nesting instability
creates phonon softening around the zone boundary.
broadenings also pick up in that region. On heating
up across the ferromagnetic $T_c\sim0.07t$, a marked
increase in lifetimes take place. The momentum
dependence of the spectrum is also subdued.
Moving to the polaronic crossover regime, the
ground state picture is roughly unaltered,
whereas thermal broadenings generally decrease,
due to formation of short-range correlations.
This effect is markedly observed moving to the
strong coupling (third column) plots. The mean
(or mode) frequencies harden and lifetimes become
limited by the bandwidth, which scales as $\frac{t^2}{E_p}$.

\subsubsection*{Acoustic phonons}

At intermediate coupling, the polaronic crossover imparts
an overall damping of acoustic phonon spectrum throughout
the Brillouin Zone (BZ). However, the effect is most drastic
around $(\pi,\pi)$, where across a wide range of temperatures,
a `box-like' lineshape emerges (Fig.10, bottom panel).
The thermal dependence of lineshapes is not very significant.
Even at $(\pi,0)$, there are large lifetimes present
along with prominent softening, especially at high T
($T/\Omega_0=3.0$).

The corresponding fitting plots of the acoustic phonons are
exhibited in Fig.11. The left column, depicting the
mean frequencies, show prominent dips at both $(0,0)$
and $(\pi,\pi)$ in the weak coupling regime.
The Goldstone mode at $\Gamma$ point is undamped (not shown
explicitly). The softening of phonon mode at $(\pi,\pi)$
owes its origin to Kohn anomaly. Close to the crossover,
broadenings increase quantitatively, due to formation of
large static distortions and consequent phonon localization.
Thermal fluctuations magnify the effect remarakably past
the ferromagnetic $T_c\sim0.06t$. Low momentum modes
are protected from scattering because of phase space
restrictions. At strong coupling, the dispersion
regains clarity to a large degree. Only on heating up to
$T/\Omega_0=3.0$, one observes significant broadenings,
near $(\pi,0)$.

\begin{figure}[b]
        \centerline{
                \includegraphics[height=3.5cm,width=8.5cm]{12a}
        }
        \caption{Fitting of acoustic phonon spectra at finite
                temperature in terms of `softenings'
                (deviation of mean frequencies ($\bar{\omega}(\vec{k})$
                form bare values) and linewidths ($\Gamma(\vec{k})$
                through the BZ trajectory $(0,0)\rightarrow(\pi,\pi)$.
                The coupling is $g_{H}/g_c=1.0$.
                Temperature increases
                in the following sequence-
                $T/\Omega_0=(1.2,1.4,1.6)$. The
                ferromagnetic transition occurs at $T_c=1.2\Omega_{0}$}.
\end{figure}
\begin{figure}[t]
	\centerline{
		\includegraphics[height=9cm,width=8.5cm]{12b}
	}
	\caption{Summary of investigations on transverse acoustic
		phonons in La$_{0.7}$Sr$_{0.3}$MnO$_{3}$. In
		panel (e) (top left), we have phonon energies in
		meV at two different temperatures ($100K$ and $375 K$).
		Also, a model calculation is shown. In panel (f)
		(top right), phonon softenings compared to low$T$
		($5K$) values are featured for several temperatures
		along the $(h h 0)$ direction in BZ. The $T_c=350K$
		marks the onset of pronounced softenings around
		$\vec{q}_{CE}$. The bottom left panel (g) shows
		corresponding linewidths, which pick up just before
		the metal-metal transition. Lastly, in panel (h)
		(bottom right), one has quasi-elastic intensitites
		quantifying short-range ordering of polarons beyond
		$T_c$.
	}
\end{figure}

\section{Discussion}

We list below the salient features of
 the phonon modes revealed through our investigation-

\begin{itemize}
\item The low temperature state of
our model is ferromagnetically ordered and
shows charge correlations at strong coupling.
\item The weak coupling `disordered
metal' at low $T$ is in proximity to a nesting
 instability for $n\sim0.5$. As a result, both
 optical and acoustic modes are softened
 considerably around $(\pi,\pi)$.
\item On heating up the weak coupling state, two
effects occur simultaneously. Firstly, thermal
fluctuations induce large static distortions in the
 optical mode. Secondly, the ferromagnetic order
  is lost as one goes across $T_c\sim0.1t$.
  This leads to broad, flat optical phonon
  spectrum and a loss of coherence (barring
  small wavevectors) in the acoustic mode.
These features are correlated with the
 appearance of a weak pseudogap in the
 electronic density of states, owing to
 spin disorder.
\item The intermediate coupling state is on
 the verge of a polaronic transition. So,
  phonon eigenstates tend to get localized.
  This results in generally broad phonon modes
  except around $(0,0)$. On increasing
  temperature, the lifetimes increase quantitatively,
  along with a flattening of the optical phonons.
  The electronic spectrum is already pseudogapped
   in the ground state, the extent of which
    becomes milder on heating up.
\item At stronger couplings, a short-range
 $(\pi,\pi)$ order sets in amongst polarons
 at low $T$. As a result, the electronic spectrum
  shows a small hard gap. There's a depletion
  of states near Fermi level, leading to weaker
  low-energy weights in the polarization
   based self-energy for the phonons.
   Consequently, both acoustic and
   optical modes regain some coherence.
   The damping is bandwidth limited
    $\Gamma\sim\frac{t^2}{E_p}$.
\item Heating up and going across the
 ferro $T_c$ (which is almost half of
  its weak-coupling value), one creates
   a more disordered background for the
   phonons to propagate. This causes
    broadening effects to pick up. The electronic
    spectrum shows a prominent pseudogap
    and the acoustic phonons are
     broadened considerably.
\end{itemize}

We've tried out a qualitative comparison with
actual experimental data for acoustic phonons in
La$_{0.7}$Sr$_{0.3}$MnO$_{3}$\cite{weber2}. Fig.
12 summarizes our results. The general
trends show an agreement. Our acoustic phonons
show increased softening and broadening effects
at intermediate coupling ($g_{H}/g_c=1.0$)
just before the ferromagnetic transition $T_c\sim1.2\Omega$
at $K$ point. This is also the important wavevector
for short-range ordering of polarons. Correspondingly,
in the experimental plots (Fig. 13), we see around
$\vec{q}_{CE}$, the softening and linewidths pick up,
just before $T_c=350K$. The increase is monotonic in
both cases along the BZ trajectories chosen.
The quasielastic intensity, which
quantifies short-range ordering of distortions,
shows a marked increase near the same wavevector
at $T_c$. On crossing this temperature, both
the theoretical and experimental curves show
a mild reduction in broadenings.

\section{Conclusions}

In conclusion, we've studied the phonon spectrum of
the weakly disordered
double exchange Holstein model in two dimensions.
The results have direct implications for recent
inelastic neutron scattering experiments in manganites.
The novelty of the method is to be able to capture
short-range correlations amongst polarons and
resulting pseudogap features in the electronic
spectrum at finite temperature. This in turn affects
the polarization of the system, which renormalize
the acoustic and optical phonons. The most interesting
region in our parameter space is one of intermediate
coupling and temperature, when polarons start forming
and the ferromagnetic order in the ground state is
on the verge of destruction. We've quantified the
observed spectrum through detailed fitting across BZ
and an analysis of lineshapes at specific high-symmetry
points. We are investigating the problem at even weaker
values of binary disorder, so as to disentangle the polaron
physics from the effect of disorder. We also wish
to compare our findings with experiments in more detail
in the future.

{\it Acknowledgement:}
We acknowledge the use of HPC clusters at HRI. SB
acknowledges fruitful discussions with Samrat Kadge
and Abhishek Joshi, and thanks Samrat Kadge for a careful
reading of the manuscript. The research of SB was partly
supported by an Infosys scholarship for senior students.
The research of SP was partly supported by the  Olle
Engkvist Byggm\"{a}stare Foundation.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


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text:
It Appears In Rutherford County The Grinch Is Alive And Well
By	Deborah Keller | December 11, 2020
Forest City: Two weeks before Christmas a young single mother has lost her job apparently because she dared to stand up for what she perceived was an injustice to a friend.
Lexie Kennedy
Lexie Kennedy organized a protest meeting for this Saturday at 3:45 pm to 5:30 pm at the Courthouse in Rutherfordton (see link) in support of Ethan Colton who was recently shot and killed by Rutherford County Sheriff's Officer Tyler Greene during a questionable arrest. According to the victim's family members he was shot in the back resulting in his death during the arrest. The SBI are currently investigating this as is the custom for all law enforcement shootings.
Sheriff Chris Frances
Emotions are running high in the community as several witnesses have a different account of what happened on the scene as opposed to the official statement released by the Sheriff's Office. In a statement released Thursday by Sheriff Chris Frances it appears that someone has been making threats to his officers concerning this incident. This if true should be investigated and those persons should be held accountable. Violence only begets violence and should not be tolerated on either side.
That being said Lexie Kennedy's story which was not about violence or threats towards the RCSO took a sad turn today. On Dec. 8th she was contacted by John Le from WLOS about being interviewed concerning the protest on Saturday. He asked if he could come to her job to talk with her. She asked her manager who said yes. She then asked her manager if she could post a Facebook live video about it during her break. She was excited that WLOS was interested in the protest. The manager told her yes as long as she did not wear any identifying items with Zaxby's on it. She complied and took off her hat, mask, and put a jacket on over her name tag.
Thursday morning at work she was contacted by Zaxby's HR who watched the video while on the phone with her and stated she found nothing wrong with the video but wanted to let her know that company policy did not allow phone usage while at work. She explained that she was on her break when she made the video.
Later in the day District Manager Jesse Ortiz came into the store and informed her she was fired for not adhering to company policy and made her sign a statement to that fact. When she questioned him as to what policy she violated he did not answer her.
After he left she asked her shift manager who was standing with the General Manager why she was fired. The shift manager said that Rutherford County Sheriff's Office called Corporate and complained that they felt threatened by her working there and could not support the business as long as she was there. The General Manager did not deny this to Ms. Kennedy.
Ethan Colton Family
She was confused as nothing in her video was threatening in any way. However when she went back to review the video it had been erased from her Facebook feed. She had received no notice from Facebook that it was removed. It was just "gone." Her freedom of speech erased by someone, somehow without her knowledge.
The loss of a job especially during a pandemic is such a sad thing for a young single mother to try to deal with two weeks before Christmas. If the reason for her dismissal was in fact because the Sheriff's Office felt threatened then they should explain how this young woman caused them to fear for their safety enough to deprive her and her children of their income at Christmas. If that was not the reason then they should lead the charge in getting this young woman her job back as the very appearance of any type of intimidation during an active SBI investigation is unconscionable.
(Photo used with permission)
Either way it appears that Zaxby's and possibly someone at Rutherford County Sheriff's Office has caused the Grinch to target this young woman and her family depriving them of Christmas. Hopefully she can find the strength in her heart to persevere through this time and realize that doing the right thing is rarely ever easy. It is always to be commended when one supports and stands up for a friend especially when that friend can no longer stand up for themselves.
In the immortal words of Dr. Seuss "Christmas Day will always be .Just as long as we have we." In a county and country looking for unity helping this one poor soul would be a start. Hopefully someone's heart can grow from this.
To contact Zaxby's see information below:
Zaxby's Forest City Store
General Manager : Marsha Rictor
District Manager: Jesse Ortiz
Zaxby's Corporate :
https://feedback.zaxbyslistens.com/?AspxAutoDetectCookieSupport=1
To contact Rutherford County Sheriff's Office:
chris.francis@rutherfordcountync.gov
If you have any questions or concerns please send them to debkellercares@gmail.com and I will attempt to get them answered for you. (all communications are confidential)
Category: Law Enforcement Opinion RC Sheriff's Department Restaurant Tags: Christmas, Ethan Colton, Grinch, Jesse Ortiz, John Le, Marsha Rictor, protest, Rutherford County Sheriff's Office, Sheriff Chris Frances, shooting, WLOS, Zaxby's
About Deborah Keller
Medical Correspondent/Independent Journalist, Author, BS in Health Services, ADN Registered Nurse (specializing in critical care), Duke University Certified Nonprofit Manager, Former EMT-I and EMT Instructor, Photographer, Graphic Designer, and Media Consultant.
View all posts by Deborah Keller →
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redpajama_set_name: RedPajamaCommonCrawl


text:
Targeted Jobs
Explore our Featured Jobs here.
Baylor Scott & White Health was founded as a Christian Ministry of Healing. The Pastoral Care teams continue this spiritual ministry by offering emotional and faith support to patients, families and staff.
Serving Faithfully
Our pastoral care teams are local to each full-service hospital, providing 24/7 access to spiritual care and emotional support during times of crisis for patients, families and staff.
Our Faith in Action team is here to strengthen the spiritual lives of Baylor Scott & White staff, as well as empower medical mission work both locally and internationally.
Acting Honestly
Chaplains abide by the Baylor Scott & White code of ethics and the professional standards for Board Certified Chaplains by the Association of Professional Chaplains as well as the Association of Christian Chaplains.
Confidential conversations are held in sacred trust within the limits of the law.
Never Settling
Our daily goal is to provide quality and compassionate Spiritual Care. We encourage and support creative ministry ideas and share best practices across the system.
Never Settling also means always learning. Our Pastoral Education team provides quality, cutting-edge Clinical Pastoral Education training in an environment where all are welcome.
We work together to provide spiritual care and emotional support for everyone who enters our doors.
The Pastoral Care department is Committed to Diversity and Inclusion as spiritual care providers serving in multicultural and multifaith communities.
Hear from our leaders
Hear from our employees
Our bragging rights are your bragging rights.
Rev. Sherwin D.
Chaplain Supervisor NTX-Frisco hospitals
"In the Office of Mission and Ministry, we are here to extend and enhance the staff, patient and visitors' experience to another level, catering to their spiritual and emotional needs. The institutional culture "we are in it together" has enabled me to work as a team and become culturally sensitive to my colleagues and patients that enter the campus for a healing experience and beyond. It is my zeal, passion and bounded duty to reach out to one another and fulfil my professional goals as a chaplain."
Rev. Leslie S.
Chaplain Supervisor NTX McKinney
"I am proud of Baylor Scott and White's mission, founded as a ministry of Christian healing, and commitment to diversity, equity, and inclusion so that together we can promote the well-being of all individuals, families, and communities. It is refreshing and a blessing to be in this healthcare system where we have mutual respect and honor for each patient, person, position, and role. It takes a team of servant leaders, on the frontline and in the background, to achieve and maintain the quality of care we deliver across so many access points. I am honored to lead, to learn, and to develop leaders while also serving the BSWH team as a spiritual care provider for patients, families, and staff caregivers."
Curtisha G.
NTX Virtual Chaplain
"I have the privilege of offering ministry to our patients and staff in a digital role. COVID-19 forced the healthcare system to recalibrate and Baylor Scott and White remains relevant as we find innovative solutions to continue to offer diversity, healing, and excellence in patient care. I started as a clinical pastoral education student in BSW's pastoral education program and then transitioned into a professional chaplain. A few of the many reasons I'm grateful to be a part of the BSW team is the constant evolvement in process improvement, collaboration, staff recognition and the freedom to contribute creatively to revolutionary initiatives. As premier leaders in our industry we explore and develop the most effective ways to accomplish our mission, the Christian Ministry of Healing."
Rev. Shirley J.
Chaplain Manager NTX Plano Regional
"As a hospital system founded from Christian Ministry, our goal is to provide best care equally for all people, those of faith and those of none. In the Office of Mission and Ministry, we support the wellbeing of our patients, families, and all of our staff. We work together as a team to serve faithfully. Working together, we can accomplish far more than we could separately. The teamwork and compassionate care we are able to provide daily is what brings me to work each day as a professional chaplain and spiritual leader."
slide 1 of 2 Margaret M., Digital Health Management Consultant II "The Digital Team at BSWH has the unique opportunity to create meaningful products for the patients we serve. Our goals are simple: to make healthcare more accessible and to improve the patient experience. I enjoy working on this team because of the passion, energy and empathy that is part of every discussion around the design, development and implementation of our products."
301 N. Washington Avenue
As a healthcare system committed to improving the health of those we serve, we are asking our employees to model the same behaviors that we promote to our patients. As of January 1, 2012, Baylor Scott & White Health no longer hires individuals who use nicotine products.
We are an equal opportunity employer committed to ensuring a diverse workforce. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, national origin, disability status, protected veteran status, or any other characteristic protected by law. To view the most recent EEO is the Law Poster, click here.
© 2021 Baylor Scott & White Health. All Rights Reserved.
533c3fb300c841e187811ed300262234


text:
Home > Artists > Thomas Rowlandson > Artwork
Jupiter & Juno
Thomas Rowlandson (1757-1827)
8 ¾ x 6 ¾ inches
Luke Gertler
'Chris Beetles Summer Show', 2020, No 9
As a student of the Royal Academy Schools in the 1770s, Thomas Rowlandson would have been required to emulate classical models by drawing from casts of antique sculpture. At the same time, he would also have absorbed many of the historical and mythological stories that such sculpture represents. He maintained these interests throughout his career, continuing to produce both serious and satirical images based on mythological subjects.
Jupiter & Juno exemplifies Rowlandson's art at its most purely neoclassical, and suggests a response to the outline illustrations by his almost exact contemporary, John Flaxman, to Homer's The Iliad and The Odyssey, published in 1793. However, it may also have been influenced by a more seductive Renaissance model, Titian's Jupiter, Juno and Io, which hung at Blenheim Palace (until it was destroyed by fire in 1861), and was reproduced by John Smith in 1709. Smith based his mezzotint most directly on an engraving by Jacopo Caroglio (died 1565). Caroglio is perhaps best known for his collaborations with Rosso Fiorentino and Perino del Vaga, including Loves of the Gods, an erotic series of prints that Rowlandson admired. Rowlandson referenced the series in his satirical print, Modern Antiques (circa 1811), in which a book with the title Loves of the Gods lies beneath a young couple embracing in a mummy case.
The king and queen of the Roman gods, Jupiter and Juno (known in Greek as Zeus and Hera) were both siblings and spouses. Rowlandson seems to show them at an early stage in their relationship, before Juno's 'conjugal happiness' became 'frequently disturbed by the numerous amours of her husband' and 'showed herself jealous and inexorable in the highest degree' (as explained by John Lemprière in his highly popular classical dictionary, Bibliotheca Classica, first published in 1788).
With thanks to Nick Knowles for contributing information to this note.
The Fiddler and His Family
Micklegate, York
Infidelity Discovered
On the Thames
Cornwall, East and West Loo[e]
Youth and Age
Symptoms of Sanctity
Fair Lane
Cries of London, 'Milk O'
A Crab Hunting For Prawns


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Mark Zimmerman is a published author. A published credit of Mark Zimmerman is How to Do Business with the Japanese.
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text:
The Resource Modern reports: : or, select cases adjudged in the courts of King's Bench, Chancery, Common Pleas and Exchequer, since the restoration of His Majesty King Charles II. to the fourth of Queen Anne. [1663-1705], In seven volumes. With two tables; the first of the names of the cases, and the other of the special matter therein contained
Modern reports: : or, select cases adjudged in the courts of King's Bench, Chancery, Common Pleas and Exchequer, since the restoration of His Majesty King Charles II. to the fourth of Queen Anne. [1663-1705], In seven volumes. With two tables; the first of the names of the cases, and the other of the special matter therein contained
The item Modern reports: : or, select cases adjudged in the courts of King's Bench, Chancery, Common Pleas and Exchequer, since the restoration of His Majesty King Charles II. to the fourth of Queen Anne. [1663-1705], In seven volumes. With two tables; the first of the names of the cases, and the other of the special matter therein contained represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Biddle Law Library.
Great Britain, Courts
Pickering, Danby, fl. 1737-1769
4th ed.
Reviewed and corrected, and many thousand new and proper references added, never before printed, from all the books of reports, down to the year 1757. By Danby Pickering.
Modern reports: : or, select cases adjudged in the courts of King's Bench, Chancery, Common Pleas and Exchequer, since the restoration of His Majesty King Charles II. to the fourth of Queen Anne. [1663-1705]
Modern reports:
or, select cases adjudged in the courts of King's Bench, Chancery, Common Pleas and Exchequer, since the restoration of His Majesty King Charles II. to the fourth of Queen Anne. [1663-1705]
In seven volumes. With two tables; the first of the names of the cases, and the other of the special matter therein contained
Law reports, digests, etc. -- Great Britain
KD200 1663.M6
fl. 1737-1769
Pickering, Danby
Law reports, digests, etc.
(OCoLC)5637300

 Data from Modern reports: : or, select cases adjudged in the courts of King's Bench, Chancery, Common Pleas and Exchequer, since the restoration of His Majesty King Charles II. to the fourth of Queen Anne. [1663-1705], In seven volumes. With two tables; the first of the names of the cases, and the other of the special matter therein contained - Biddle Law Library

Data Citation of the Item Modern reports: : or, select cases adjudged in the courts of King's Bench, Chancery, Common Pleas and Exchequer, since the restoration of His Majesty King Charles II. to the fourth of Queen Anne. [1663-1705], In seven volumes. With two tables; the first of the names of the cases, and the other of the special matter therein contained
http://link.law.upenn.edu/portal/Modern-reports--or-select-cases-adjudged-in/C7Bpr2MxmM4/
http://library.link/portal/Modern-reports--or-select-cases-adjudged-in/C7Bpr2MxmM4/


text:
/*	$Id: main.c,v 1.14 2001/08/10 15:18:08 sandro Exp $	*/

/*
 * Copyright (c) 1997-2001 Sandro Sigala.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * Changes by HLG
 */

#include "config.h"

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <sys/types.h>
#include <errno.h>
#include <time.h>
#include <err.h>
#include <getopt.h>
#include <signal.h>
#include <setjmp.h>

#ifdef HAVE_READLINE
#include <readline/readline.h>
#include <readline/history.h>
#endif

#include "slisp.h"
#include "extern.h"
#include "version.h"
/* global variables */

int done;
int opt_lint = 1;
int opt_verbose = 0;

extern int used_objs;

jmp_buf env;
static void process_input(void);
extern char *randomstring(void);
extern void usage(void);
extern void print_logo(void);
/* required by -ansi :S */

extern int mkstemp(char *);
extern int kill(pid_t, int);
extern void _rl_enable_paren_matching(int);
extern char *progname;

extern void handsig(int sig)
{
    longjmp(env,sig);
}

#ifdef HAVE_READLINE
char *buffer; /* Contains the buffer to be parsed */

static  char *line_read = (char *) NULL; /* need this! */

/* yeah, very very stupid function */

__inline__ int getchl(void)
{
    int c;
    c=(int) *buffer;

    if(c == '\0')
	    return EOF;

    buffer++;
    return c;
}

/* Well we have to check  if the buffer has the same number of opened
   parenthesis as closed ones. Unless it returns 1, the buffer is not
   completed, so not evaluaded
*/

int donep(char *s)
{
	int op,cp; /* op: opened parenthesis, cp: closed parenthesis */
	int i;
	int len;
	op=cp=0;
	len=strlen(s);

	for(i=0;i<=len;i++) {
		if(s[i] == '(')
			op++;
		else if(s[i] == ')')
			cp++;
	}
	if(op > cp)
		return 0;
	else
		return 1;
}

__inline__ char *rl_gets ()
{
    if (line_read) {
	    free(line_read);
		line_read = (char *)NULL;
    }
    line_read = readline (">> ");
    return (line_read);
}

void initialize_readline (void)
{
	rl_readline_name = "";
	rl_bind_key('\t',rl_insert);
	rl_bind_key('\n',rl_insert);
	_rl_enable_paren_matching(1);

	rl_set_paren_blink_timeout(750000);
}

static void process_input(void)
{
	objectp p, p1;
	char *next;
	int onatty = input_file == stdin && isatty(STDIN_FILENO);
	buffer=(char *) calloc(1024,sizeof(char));

	initialize_readline();
	init_lex();

	if(setjmp(env) == 0) {
	  LOOP:
		for (;;) {
			if (onatty) {
					/* if thereis something to read ...*/
				while(!buffer || !*buffer) {
					buffer=rl_gets();

					while(donep(buffer) == 0) { /* if its not done */
					    next=readline("   ");/* read more */
					    strcat(buffer," ");/* put a space between lines */
					    strcat(buffer,next); /* append to the buffer */
					}
				}
				/* you think is a redundancy, but if rl_replace_line() */
				/* fails, it will cause a segv */
				if (buffer && *buffer) {
					add_history (buffer);
				}

			}
			if ( (p = parse_object(0)) == NULL) {
				if( input_file == stdin) {
					goto LOOP;
				} else
					break;
			}

			if (opt_verbose) {
				printf("<= ");
				princ_object(stdout, p);
				printf("\n");
			}

			p1 = eval(p);
			if (onatty || opt_verbose) {
				printf("=> ");
				princ_object(stdout, p1);
				printf("\n");
			}
			if(!onatty) {

#ifdef DEBUG
				warnx(":: objects before collection");
				print_obj_lists();
#endif
			}
			garbage_collect();

			if(!onatty) {
#ifdef DEBUG
				warnx(":: objects after collection");
				print_obj_lists();
#endif
			}

		} /* end for */
	} else {
		buffer="t\n";
		goto LOOP;
	}
	done_lex();
}
/* don`t have readline */

#else

static void process_input(void)
{
	objectp p, p1;
	int onatty = input_file == stdin && isatty(STDIN_FILENO);

	init_lex();

	for (;;) {
		if (onatty) {
			printf(" >> ");
			fflush(stdout);
		}

		if ((p = parse_object(0)) == NULL)
			break;

		if (opt_verbose) {
			printf("<= ");
			princ_object(stdout, p);
			printf("\n");
		}

		p1 = eval(p);

		if (onatty || opt_verbose) {
			printf("=> ");
			princ_object(stdout, p1);
			printf("\n");
		}

#ifdef DEBUG
		warnx(":: objects before collection");
		print_obj_lists();
#endif
		garbage_collect();
#ifdef DEBUG
		warnx(":: objects after collection");
		print_obj_lists();
#endif
	}

	done_lex();
}
/* endif of HAVE_READLINE */
#endif

int process_file(char *filename)
{
	if (filename != NULL && strcmp(filename, "-") != 0  && strcmp(filename, "--") != 0) {
		if ((input_file = fopen(filename, "r")) == NULL)
			return -1;
	} else
		input_file = stdin;

	process_input();
	if (input_file != stdin)
		fclose(input_file);
	return 0;
}

int pro_file(char *filename)
{
	if (filename != NULL) {
		if ((input_file = fopen(filename, "r")) == NULL) {
			warn("%s",filename);
			return -1;
		} else {
			printf(";; Loading file %s\n",filename);
		}
	}
	return 0;
}

int main(int argc, char **argv)
{
	int next_option;
	int fd;
	char buildf[]="/tmp/slisp.XXXXXX";
	char *file;
	FILE *init_file;

	int no_init = 0;
	int p_only = 1;
	int display_ascii = 1;
	int no_build = 0;

	const char* const short_options = "hqVNiBbvpx:";
	const struct option long_options[] = {
		{ "help",     0, NULL, 'h' },
		{ "quiet",    0, NULL, 'q' },
		{ "version",  0, NULL, 'V' },
		{ "no-warnings", 0, NULL, 'N' },
		{ "process" , 0, NULL, 'i' },
		{ "no-build-in", 0, NULL, 'b' },
		{ "no-init-file",0, NULL, 'p' },
		{ "verbose",  0, NULL, 'v' },
		{ "exec", 1, NULL, 'x' },
		{ NULL,       0, NULL, 0   }
	};
	signal(SIGUSR1,handsig);
	signal(SIGINT,handler);

	do {
		next_option = getopt_long (argc, argv, short_options,
					   long_options, NULL);
		switch (next_option)
		{
		case 'h':
			usage ();
		case 'q':
			display_ascii = 0;
			break;
		case 'V':
			fprintf(stderr,"%s\n",SLISP_VERSION);
			exit(0);
			break;
		case 'v':
			opt_verbose = 1;
			break;
		case 'N':
			opt_lint = 0;
			break;
		case 'i':
			p_only = 0;
			display_ascii = 1;
			break;
		case 'b':
			no_build = 1;
			break;
		case 'p':
			no_init = 1;
			break;
		case 'x':
			p_only = 1;
			display_ascii = 0;
			opt_lint = 1;
			no_build = 1;
			opt_verbose = 1;
			if((fd=mkstemp(buildf)) > 0) {
			    if( write(fd,optarg,strlen(optarg)) == -1) {
				fprintf(stderr,"error evaluating %s\n",optarg);
				unlink(buildf);
				return -2;
			    }
				process_file(buildf);
				unlink(buildf);
			} else {
				fprintf(stderr,"error evaluating %s\n",optarg);
				return -2;
			}
			return 1;
			break;
		case -1:
			break;

		default:
			exit(-2);
		}
	}
	while (next_option != -1);

	argc -= optind;
	argv += optind;

	if(display_ascii == 1)
		print_logo();

	init_objects();
	if(no_init == 0) {
		file = (char *) xcalloc(521,sizeof(char));
		/* this is for avoid possibly exploits. It's common to exploit
		   programs that read environment variables setting values with
		   shellcodes hehe :P
		*/
		if(strlen(getenv("HOME")) >= 128) {
			warnx("your home path is just too long. :P");
			file = (char *)NULL;
		} else
			file = getenv("HOME");
		if(file != NULL) {
			strcat(file,"/.slisprc");
			init_file=fopen(file,"r");
			if(init_file!=NULL) {
				fclose(init_file);
				process_file(file);
			}
		}
	}
	if(no_build == 0) {
		if((fd=mkstemp(buildf)) > 0) {
			if( write_m(fd) != 0) {
				unlink(buildf);
				warnx("%s",write_m);
			}
			process_file(buildf);
			unlink(buildf);
		} else
			warnx("cannot load build-in functions\n");

	}
	if (argc < 1)
		process_file(NULL);
	else {

		while (*argv) {
			if(process_file(*argv) != 0) {
				warn("%s",*argv);
			} else {
				printf(";; Loaded file %s\n",*argv);
			}
			argv++;
		}
	}
	if(p_only == 0)
		process_file(NULL);
	return 0;
}

redpajama_set_name: RedPajamaGithub


text:
Santiago Gallo fue un industrial azucarero y político tucumano. Nació en San Miguel de Tucumán en 1851 y falleció en 1909. Entre 1884 y 1886 fue gobernador de la Provincia de Tucumán, Argentina.

Biografía
Perteneciente a la oligarquía tucumana, se crio en San Miguel de Tucumán junto con su hermano Delfín Gallo.

A diferencia de su hermano, sus actividades estaban concentradas en la industria azucarera. Estaba a cargo de dos ingenios en Tucumán, Luján y El Colmenar, y uno en Santiago del Estero, el ingenio Contreras.

Asumió como gobernador de Tucumán el 12 de octubre de 1884, como sucesor de Benjamín Paz. Al ser opositor de Miguel Juárez Celman, fue muy resistido en su cargo. Por esta razón, sus enemigos acudieron a la recién vigente Constitución de Tucumán , cuyo artículo 13 decía que el gobernador actual debía cumplir su período hasta el fin, pero que el sucesor ya debía amoldarse a la nueva constitución. Si se referían a Benjamín Paz, a quién faltaban pocos días para cesar su mandato cuando se sancionó la constitución, a Gallo le quedaban tres años de mandato. Si se refería a Gallo, le correspondían solamente dos años. La cuestión fue zanjada por el Colegio Electoral Permanente que dictaminó que el gobernador debería permanecer tres años. Sin embargo, la oposición solicitó al Congreso la intervención Federal.

El presidente Julio Argentino Roca respetó a los opositores tucumanos, pero le advirtió al diputado por esa provincia, Delfín Gallo, que no podía garantizar que ocurriera lo mismo después de su presidencia.

En junio de 1886, Juárez Celman fue consagrado presidente. De acuerdo a lo convenido con Roca, el 3 de septiembre, Gallo renunció a la gobernación y fue reemplazado por alguien más cercano al "juarismo" como era el industrial Juan Posse.

Referencias
La Gaceta - Renuncia del gobernador Gallo

Gallo
Gallo
Gallo

redpajama_set_name: RedPajamaWikipedia


we love our roddy sofa and love seat, great color and very comfortable. thank you joybird!
WE LOVE OUR RODDY COUCH!!!!!!!!! It couldn't fit any better into our design scheme and personal style if we tried! It is so comfortable, stylish, handsome, well-made and the color.... well, I think this photo speaks for itself. Thank you from the top of our hearts to the bottom of our butts that sit on our amazing, new, Key Largo Kelly Green, Roddy Couch!
I love the ottoman. Matches perfectly. It definitely makes the couch more comfortable.
Absolutely love my Roddy loveseat! At first I thought it was a bit too firm but it's getting more comfy by the day. I must admit I was skeptical about ordering a couch sight unseen but I can't say enough about the quality of this piece. Love the style, color, and fabric. Delivery and setup went very smoothly. Take the chance, you won't regret it! Thanks to everyone at Joybird!
The pillows haven't come yet, but the loveseat is nice.
Great couch; color was exactly as described; very comfortable!
I've had this for about a year and it's amazing! Perfect length for naps. Comfortable for sitting. The cats love it. It's the first thing people see and compliment when they visit. Completely changed the way I viewed furniture -- your pieces should look great, feel great, last a long time, and exude awesomeness.
This sofa is great for us. The fabric has the variation and vibrancy I was looking for. This is not a Netflix couch. This is the type of couch you have for when you have a people over. 4 people can sit on this couch without feeling to physically close. The cushion is stiff so you do not get the smoosh factor, I hat sitting next to someone and being forced together by the collapse of the stuffing under me. I am a small person and this couch is a good fit or me. The art piece is made by Christopher Konecki.
Roddy sofa in key largo coral. With the richness of navy that correlates with our Hopson apartment sofa and Soto apartment chair, our small living area is transformed into a warm and cozy boho space.
Love my Roddy sofa! So perfect with my mid century modern coffee table find!
Stunning Roddy Sofa in Taylor Golden! Love Love Love it! it has been a long wait but so worth it. Thank you Joybird for this amazing piece that we love!
This is absolutely beautiful... it looks better than I expected! Really comfortable! My family loves it!
I love the look of this sofa and it looks amazing in my living room. I really wanted a structured couch that would always have clean lines. This ended up being perfect. I loved having the ability to pick 70+ different fabrics and thought the free swatches were an awesome touch. I have often had to pay for swatches from other companies. It's great of joybird to send them out for free. I will definitely buy from them again and have told numerous people about my awesome experience buying this couch.
My Roddy Sofa is definitely a conversational piece for my living room. I purposely chose grey as my base color so pillow/rug options would be limitless. I've order a grey and white stripped colored blanket to add to my relaxation.
The Appletini Roddy sofa works great in my living room. It is wide, sturdy, comfortable and eye-catching. What a great addition! Thanks Joybird!
My sofa is gorgeous. It did not fit in my front door, so I would recommend measuring better than I did and add a buffer. We ended up have to take the bottom of the frame off (the legs) and carry it in as two pieces and reassemble. Otherwise the construction is great, and it is very high quality. Super firm.
It took a loooong time for us to decide on a sofa. We finally took the plunge and ordered a sofa online. We've had the Roddy for a week. We really love the look. Everyone gushes about it when they visit. I gave it four stars for service, delivery, style, and comfort. I'll keep the last star for quality; that will take a period of use to determine.
Beautiful couch, totally worth the fabric upgrade!
It's very firm and comfortable. I like how it's one piece, without removable cushions.
Cute kid and new couch! Yippee!!
The couch is awesome. Great color. Great build. Super comfortable.
I picked Elizabeth Ocean and the fabric is gorgeous! This is the first piece I have purchased for this room. I absolutely love it!!
It's here, we love it! It was definitely worth the wait. Thanks, Joybird!
My dogs practically owns the sofa! Very durable and comfy!
The Roddy sofa is gorgeous! I am very pleased with the quality of craftsmanship, and it is super soft! It fits right in our living room.
Arrived as beautiful as expected. Great communication throughout. A great experience!
LOVE LOVE!! Got it earlier than expected and JB Hunt did an awesome job getting it here!
Take a look behind the scenes to see how our products are handmade. Get an in-depth looks into our factory and see the talented craftsmen working on your piece.
The Roddy's carefully cushioned back is molded into a slight recline to provide natural support.
The tight back and seat still deliver on settle-right-in coziness, without loose cushions.
Long, lean, and chic, the Roddy collection uses its sharp shapes and splayed wooden legs to spread its style around the room. Elegant button tufting brings a little something extra to this collection's distinctly retro profile that has already stood the test of time.


text:
COVID-19: Donald Trump's Heavy Responsibility for American Massacre
Published in Le Monde
(France) on 16 January 2021
by Editorial [link to original]
Translated from French by Paul Naanou. Edited by Gillian Palmer.
The death toll of 400,000 apparently results from of the arrogance, cynicism, contempt for scientists and lies characteristic of the [former] American president.
Just four years ago, Donald Trump promised a shocked world that "American carnage stops right here." The night before departing the White House, the Republican president leaves a country in shambles behind him, ridden with rarely rivaled divisions and entrenched in unheard of political violence, and above all else, destroyed by a stealthy pandemic that is totally out of control in certain locations.
His management of the health crisis, defined time and time again by indifference, denial, lies and politicization, leaves the United States with numbers unlike those in the rest of the world: more than 400,000 deaths in 11 months, and 23 million people infected.
As for the rest, by denying the gravity of a virus that he contracted himself, by claiming despite all evidence that "like a miracle, one day it will disappear," by obstinately refusing to promote basic precautions — wearing masks and social distancing — and by giving priority to economic interests over the risk to public health, the exiting president encouraged a deathly laissez-faire attitude in the states governed mainly by Republicans, and complicated the task for newly elected officials, many of whom are Democrats, determined to fight the pandemic.
The current carnage therefore appears to be the consequence of a mixture of arrogance, cynicism, contempt for scientists and shameless lies characteristic of Trump's personality, the first leader ousted because of his catastrophic choices concerning COVID-19.
Biden's Empathy
Joe Biden will inherit this grim record. His first weeks in the White House where he takes up residence on Jan. 20, will be completely devoted to fighting the pandemic and working toward recovering the American economy. The Democratic president, mocked by his opponent for wearing a mask and taking precautionary measures against COVID-19 since last spring, gave a solemn speech on Jan. 14 detailing the measures he plans to take to contain the spread of the virus. Biden promised financial and logistical efforts in order to better distribute the vaccine, to improve protocols for testing and tracing, and to fight against new variants of the virus.
Once again, Biden also showed the empathy that his predecessor was incapable of during these last 11 months during which almost 400,000 American families lost one of their own. But comforting words won't be enough. Biden will have to get his bailout plan passed by a Congress torn by the impeachment of an incumbent president after his supporters assaulted the Capitol.
While the virus is surging again in several countries, there is no miracle cure that will allow us to wash our hands of it so quickly. The Democratic president's team is not without its strengths, however. His incoming chief of staff, Ron Klain, coordinated the federal response to the Ebola virus in 2014, and his main advisers are all familiar and respected experts. It is to be hoped that this administrative coherence will improve federal strategy and through example, give the country clear guidelines, a discourse based on science, and a solution based in reality. Something quite the opposite of the lies and procrastination we received from the outgoing president.
COVID-19 Vaccine Racism


In order to install Audacity, you need to download the program and some extra files.
1. Go to Audacity's web page (http://audacity.sourceforge.net/download/) and click on the "Windows" link.
2. Click on "Descargar" (download).
3. Click on the "Instalador" file corresponding to your Operating System.
4. Select "Guardar archivo" (Save file).
5. When the download operation is complete, double-click the downloaded file (audacity-win-unicode-1.3.12.exe, remember the numbers may change if the file has a newer version) and follow the normal install steps.
6. Your Audacity is correctly installed. Now we need to add one little file that is really useful.
7 . Go back to the "Descarga" (Download) page on step 3 and click on "Codificador LAME MP3", and follow the instructions until you find this file: audacity-win-unicode-1.3.12.exe (remember the numbers may change if the file has a newer version). Download this file.
8. Double-click the file and install it.
9. Now you have Audacity AND you can export Audacity files as MP3.
10. Start Audacity and record a sample of your voice. Click on the Record button and start your sound. When you finish, you can click on the Stop button.
11. Now you have a sound track. You can listen to it by clicking Play. The other buttons (Pause, Home and End) allow you to "navigate" your recorded track.
12. To save a track, click Archivo (File) and Exportar (Export). Save your file with the MP3 type.
You can now record sound as many times as you want.


text:
SKIP_TO_MAIN_CONTENT
Maccabiah
Maccabiah History
Maccabiah Stories
Seventh Maccabiah 1965 | August 23 - 31
First Maccabiah
Second Maccabiah
Third Maccabiah
Fourth Maccabiah
Fifth Maccabiah
Sixth Maccabiah
Seventh Maccabiah
Eighth Maccabiah
Ninth Maccabiah
Tenth Maccabiah
Eleventh Maccabiah
Twelfth Maccabiah
Thirteenth Maccabiah
Fourteenth Maccabiah
Fifteenth Maccabiah
Sixteenth Maccabiah
Seventeenth Maccabiah
Eighteenth Maccabiah
Nineteenth Maccabiah
Twentieth Maccabiah
The Seventh Maccabiah:  5725
With 1,200 athletes from 25 countries participating, the Seventh Maccabiah attained the highest level of achievement of all competitions since WWII.  For the first time, delegations arrived from Venezuela and Peru and at the last moment, for the first and last time, Iran.  The Turkish delegation, on the other hand, was absent since the Turkish Foreign Ministry refused to grant exit visas to the basketball team.
During this, the Seventh, 22-event Maccabiah, many records set at the Sixth Maccabiah were broken.  The United States delegation, 200 strong, was outstanding, particulary in swimming, winning 14 Gold Medals in eighteen races.  Israel won three and Australian John Stark, one.  Fifteen year old Mark Spitz, appearing for the first time, won four Gold Medals and broke three records.  Another outstanding American swimmer was Olympic Silver Medal winner Marilyn Rumnovsky.  The South African gymnast, Lorraine Lutzoff, won three Gold Medals and Chana Shazifi, nee Tzadik, later one of Israels great athletes, won the 800 meter run.  Promising basketball player, 22-year old Tal Brody, played for the US team.  Only when he returned to the United States did he abandon his amateur status to play for Baltimore.
By order of the Israeli Defense Forces, a synagogue was set up in Kfar Maccabiah for the athletes.  Ramat Gan Stadium was enlarged to seat 53,000 spectators.  Hundreds of thousands of square meters of earth were moved to build huge embankments and dig tunnels. The most highly perfected athlete track was dedicated.  The dressing rooms were also enlarged and renovated.  Huge parking lots were prepared alongside the stadium, and, at the very last minute Galit Pool behind the basketball stadium in Yad Eliahu was readied for the competitions.
Baseketball games were held on six courts, mainly in Yad Eliahu Stadium.  Soccer competitions took place in five different cities.  Judo and boxing were held in rings set up on the modern basketball courts.  This time, the 8 indoor sports events were held on the fair grounds.  The first Israeli shooting range and alleys which met international standards were built in Ramat Gan.  The judo matches were among the main attractions.  Thirteen countries entered, in contrast to previous Maccabiot, when the turnout was so small that matches were held in Army bases.  Golf matches and clay pigeon shooting competitions were introduced for the first time at this Maccabiah.
West German television filmed all the performances and competitions and televised them in a special program, ׂThe Jewish Olympics׃ on the main channel.  Holland, Belgium, France, Austria and Switzerland acquired television rights.   Although the President of Israel, Zalman Shazar, opened the games in the traditional manner, a new element was added to the ceremony.  The 12-man Color Guard now consisted of two outstanding athletes from each of the previous Maccabiot.  Army parachutists staged festive landings into the stadium grounds.  The Closing Ceremony ended with the traditional soccer game, this time between the Israeli all-star team and Torino Italy (2:1).  For the first time, however, the athletes marched with comrades in their sport rather than as a nation.  Four Kenyan track and field stars, among them the best in the world, were invited to participate in the closing exhibition competitions at the conclusion of the official competitions.
As usual, the Maccabiah organizers were plagued by financial difficulties and institutional indifference.  The Israeli government contributed only 8% of the budget, 4,200,000 Israeli pounds, despite the fact that the Maccabiah Games had brought at least 10,000 tourists to Israel.  The Jewish Agency, the Jewish National Fund and Keren Hayesod did not contribute at all.  That year, in the mid-60's the new Knesset building was completed in Jerusalem and Teddy Kollek was elected mayor of the city.
Who we areOrganizing CommitteeMaccabiah HistoryInternational CommitteesMaccabiah Stories
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text:
Q: Flume hdfs sink I am trying to use Flume with hdfs as sink. File is getting exported. But I want to customize the name of the output file. I am using hdfs.filePrefix property for it. It is always creating a file with FlumeData.timestamp.

A: Please paste your configuration.
I tried it and it did work.
My setting:
agent.sinks.flumeHDFS.hdfs.filePrefix = stackoverflow

and I get the expected result.

redpajama_set_name: RedPajamaStackExchange


On a river cruise we pass many interesting sights and have many questions: What is the name of this town? How many people live in this town? When will we reach the next lock? How high is this lock? What is the name of this castle? When was this castle built? When will we reach the next port of call?
River mApp has the answer to all your questions.
Follow our real-time, interactive river map and tap on the "Points of Interest" icon and a pop-up link will appear which indicates exactly the town, castle, statue, lock, power station, bridge or historical monument you are passing. Tap on the web link and you are automatically directed to the information page of the sight you are admiring.
Our beautifully designed Apps make sure that you always know where you are, what you are looking at and where your cruise ship is heading. Thanks to our Apps your dream cruise will be even more enjoyable!
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