I tried not to write up too many stacks as I don't feel it's a good day for offense in general. That said, the Twins would be the next one on the list. Gausman prefers Caleb Joseph to catch him and today he has rookie Chance Sisco (who they are high on) catching him. The Twins are in a good spot none the less. Dozier-Rosario-Sano-Buxton and LoMo would be the core players to focus on. I like Dozier and Rosario the most as I noted them below.
We have our leader in the clubhouse for worst slate of the year.
Sundays are the best day of the week for MLB DFS if you ask me. I love them. That said, today is one of the odd-ball ones. Not only is it Easter Sunday but it's also the first Sunday of the year. Today, Mothers Day and Fathers Day seem to be the three weird ones to me….
My Sunday article's are ALWAYS for the MAIN slates. Today that is 7 games and there's not much on the afternoon slates, so no write-ups on them.
DraftKings is including the Houston @ Texas game on their MAIN slate, so they have 8 games. These guys aren't available on the FD main slate.
I am giving simply the spots that could have a PPD risk here. If there is a MAJOR weather impact then I will note that as well, however noting things like slight winds out here or slight winds out there isn't something I'm gonna feel you need to worry about here as I've factored it into my analysis below.
Pittsburgh @ Detroit should get played. They have a double-header and the Pirates obviously aren't coming back to Detroit this season. But it's really cold here.
Jose Quintana … More of a play on FD where he is a steal and highly likely to give you both the QS and the WIN. The Marlins have shown to be pesky early in the season but I don't see them doing much today on Quintana.
Jose Berrios … In terms of talent, he's the best arm going today. I hate the ballpark he has to pitch in today but the Orioles haven't exactly come out on fire to start the season. I don't mind rolling Berrios on FD. But definitely do an Orioles hedge stack in this ballpark if you roll here.
Luke Weaver … I really question if he is going to go 6 innings or more today. He has a ton of K upside but often has issues keeping his pitch count down.
Trevor Williams … T-Will the thrill! Really bad hitting conditions today and with a doubleheader we could see him allowed to get stretched out a little bit longer to save some arms for the second game of the day. He's only 5200 on DK, so he's my automatic plug in with Quintana on DK as that allows me to get the bats I want. The Tigers lineup does not scare me at all.
Jacob Faria … I like the Rays bats as a sneaky play today and Faria showed some solid flash last year when he came up. Good spot to take him today at low ownership as an SP2.
Cubs – I hate teams in South Beach on Sundays after they partied on Saturday night. Rizzo and Bryant though are locked in and Addy Russell is in a great spot today. I don't expect the Cubs to go off though. Not after two long games.
Astros – I'm not that high on them today.
The players listed next to the team are the primary ones I am looking at.
Solid ballpark, solid weather and a pitcher changing leagues making his first start of the year. Lots of hype around Gerrit Cole coming over to Houston and how Houston's video and analytics departments improved Verlander last year. That's fine and grandy, but start #1 is the time I want to pick on Cole. Not to mention the fact that we gotta find some offense and there's a ton of cold or bad ballparks on this slate today. Texas is not one of those. 73 degrees and a solid ballpark.
Steven Matz has not had a good career thus far and one can't imagine the Cards coming out and getting swept to start the season. The wind is playing well for lefties which doesn't help the Cardinals today, but the four righty bats I listed above would be a nice stack to roll out today. Good power versus the lefty Matz and the Cardinals should put up a bunch of crooked numbers early.
Hector Velazquez is basically making a spot start for Boston today and the Red Sox bullpen hasn't been great over the first few games of the season. He'll likely get bumped out early and the Tampa lineup is one that nobody will look at today. One thing to focus on here is not searching for 5 home runs with Tampa. It's not a great ballpark and Velazquez gets a ton of ground balls. Wilson Ramos has some great pop batting 7th and is a nice option on DK where you have to roster a catcher.
Kris Bryant – Has started off white hot. Costs you a pretty penny on DK today though so I am fine with the fade.


text:
Ormsby Brunson Thomas (August 21, 1832October 24, 1904) was an American lawyer, Republican politician, and Wisconsin pioneer.  He was a member of the United States House of Representatives for three terms (1885–1891), representing Wisconsin's 7th congressional district.  He also served five years in the Wisconsin Legislature and 13 years as district attorney of Crawford County, Wisconsin.

Early life and career
Ormsby Thomas was born in Sandgate, Vermont, but moved to the Wisconsin Territory with his parents when he was a young child.  His parents settled in Prairie du Chien, in Crawford County.  After receiving his early education, he was sent to the Burr Seminary in Manchester, Vermont, for an academic education.  He then graduated from the State and National Law School in Poughkeepsie, New York, in 1856.  He was admitted to the bar in Albany, New York, that year.  He returned to Prairie du Chien to establish his own law practice.

He became active in local politics and was elected district attorney of Crawford County in 1858, running on the Democratic Party ticket.  He was subsequently re-elected in 1860.

Civil War service
When the American Civil War started, in 1861, Thomas was the incumbent district attorney in Crawford County and was running for Wisconsin State Assembly.  He was elected to represent Crawford County in the 1862 session of the Wisconsin Legislature.

After the end of the 1862 legislative session, Thomas went to work raising a company of volunteers for the Union Army from Crawford County.  His company was enrolled as Company D in the 31st Wisconsin Infantry Regiment, and Thomas was formally commissioned captain in September 1862.  For the first several months of their service, the regiment was solely tasked with training for battle, supervising conscription of draftees, and guarding Confederate prisoners of war at camps in Wisconsin.  The regiment was reorganized at Racine, Wisconsin, in the Winter of 1862–1863, and mustered into federal service.

They were sent to the western theater of the war and assigned to protecting supplies and logistics in Middle Tennessee through all of 1863.  Thomas resigned his commission in January 1864 and returned to Wisconsin.

Postbellum years

On returning to Wisconsin, Thomas was elected to another term in the Assembly, but was now running on the National Union Party ticket.  This was a short-term alliance of Republicans and Pro-Union Democrats.  Thomas served in the Union caucus in the 1865 session of the Legislature and remained associated with the Republican Party for the rest of his life.  He was not a candidate for re-election in 1865, but was elected to another term in the Assembly in 1866.

After the legislative session in 1867, Governor Lucius Fairchild appointed Thomas to fill the vacant district attorney post in Crawford County, following the resignation of Joseph M. Wilcox.  He served the remainder of Wilcox's term and was then elected to another term in 1868.

In 1869, he ran for Wisconsin State Senate in the 30th State Senate district, but was defeated by Democrat George Krouskop.  He subsequently was elected to another term as district attorney in 1870.  In 1872, he was a presidential elector for Ulysses S. Grant.

During the 1870s, Thomas was focused on his legal practice.  He formed a partnership with Charles S. Fuller in 1876, which became a prominent and leading practice throughout the state.  Fuller was later appointed a county judge in the 1880s.

Thomas resumed his political career in 1879, running for Wisconsin State Senate in the 4th State Senate district, which comprised Crawford County following the 1876 redistricting law.  Thomas was easily elected running on the Republican ticket; he received 56% of the vote in a three-person race.

Congressional career

Thomas did not run for re-election in 1881, and in 1882, he waged a campaign for nomination to Congress, from Wisconsin's 7th congressional district.  His principal opponent was believed to be Gideon Hixon, who had the support of delegates from La Crosse County, but after 29 ballots at the Republican 7th district convention, the delegates broke in favor of Cyrus M. Butt, of Viroqua.  Butt went on to lose the general election to Democrat Gilbert M. Woodward.

Two years later, Thomas made another run for congress.  This time, he won the nomination on the first ballot at the convention.  He went on to defeat Woodward in the general election with 52% of the vote.  He was subsequently re-elected in 1886 and 1888, serving in the Forty-ninth, Fiftieth, and Fifty-first congresses.  During the 51st Congress, Thomas was chairman of the House Committee on War Claims.  He was defeated seeking a fourth term in 1890, in the wave election that saw Democrats claim 8 of Wisconsin's 9 congressional seats.

After leaving office, he resumed his legal career with his old partner, Judge C. S. Fuller.  Fuller, however, committed suicide in 1897.  In 1898, Thomas accepted the Republican nomination for another term as district attorney of Crawford County, and was elected in the Fall.

During his final term as district attorney, Thomas suffered from Bright's disease.  His health continued to deteriorate after he left office in January 1903.  He died at his home in Prairie du Chien on October 24, 1904.  At the time of his death, he was described as the oldest member of the State Bar of Wisconsin.

Personal life and family
Ormsby B. Thomas married Sarah E. Rosencrans at Prairie du Chien in June 1875.  They had three children together before her death in 1884.  Their first child, however, died in infancy.

Electoral history

Wisconsin Senate (1869)

| colspan="6" style="text-align:center;background-color: #e9e9e9;"| General Election, November 2, 1869

Wisconsin Senate (1879)

| colspan="6" style="text-align:center;background-color: #e9e9e9;"| General Election, November 4, 1879

U.S. House of Representatives (1884–1890)

References

External links

 Thomas, Ormsby Brunson 1832 - 1904 at Wisconsin Historical Society

1832 births
1904 deaths
People from Sandgate, Vermont
People from Prairie du Chien, Wisconsin
State and National Law School alumni
Union Army officers
People of Wisconsin in the American Civil War
Wisconsin lawyers
District attorneys in Wisconsin
Republican Party members of the Wisconsin State Assembly
Republican Party Wisconsin state senators
Republican Party members of the United States House of Representatives from Wisconsin
19th-century American politicians

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}
Entanglement or inseparability of composite quantum systems is a
characteristic trait of quantum mechanics lacking in classical
mechanics, and then becomes a key resource in many quantum
information processing protocols. The degree of entanglement
or mixture is the central concern from the
viewpoints of quantum information and quantum computation. Thus,
it is of great importance to search for a proper mathematical
frameworks to quantify such features in general mixed quantum
states. A step toward this goal is to find the criterions to
distinguish between quantum and classical correlations of mixed
states. A {bipartite} state is said to be separable if the
total density matrix $\rho_{AB}$ can be written in the form,
$\rho_{AB}=\sum_i p_i\left(|\phi_i\rangle\langle\phi_i|\right)_A
\otimes \left(|\psi_i\rangle\langle\psi_i|\right)_B$  with
$p_i>0$. Two subsystems $A$ and $B$ are said to be quantum
entangled if they are not separable. One criterion of the
separability  was proposed by Peres~\cite{Per} and later further
extended by Horodecki~\cite{Hor,Hor2} in the case of discrete variable
quantum systems in finite-dimensional Hilbert space. The
application of Peres-Horodecki criterions to continuous variable
systems in infinite-dimensional Hilbert space~\cite{Simon} has
also received much attention. Some other entanglement measures
such as negativity~\cite{Vid} and logarithmic
negativity~\cite{Ple,Eis,Vir} are also suggested for general
{bipartite}
states.

The quantum-mechanical degrees of freedom unavoidably couple to environments or baths, which induce dissipation and
decoherence.  The effective theory can be described by the reduced
density matrix, which is obtained by tracing out  environmental
variables in the full density matrix using the method of
Feyman-Vernon influence functional \cite{Fey}, and becomes an
essential quantity for constructing the entanglement measures
mentioned above.  This concept has been used in pioneering works
on quantum Brownian motion and general open quantum systems
\cite{Cal,Cal2,Cal3}. {Recently} there have been remarkable experiments
\cite{Gro1,Tho,Gro2,Nai} using an opto-mechanical resonator to
engineer the properties of the environmental degrees of freedom
and its coupling to the probed systems, which make it possible to
couple with several different baths, and to tailor decoherence and
dissipative properties in such an experimentally controlling
manner. {Thus, the experimental advances motivate theoretical
studies, showing that coupling to different non-equilibrium
environments can lead to the persistence of entanglement in the
high temperature limit~\cite{Gal,Est,Ved}. The idea is to consider
the model of two coupled, parametrically driven, dissipative
harmonic oscillators with the typical energy scale $E$, which
couple  to its own heat bath at the same temperature $T$. {It is
expected that} when $k_B T
> E$, the quantum nature of the system such as superposition and
entanglement will be lost. {However,} it was
argued that the nonequilibrium dynamics can bring the system into
the late-time saturation
characterized by an effective temperature, which is the relevant
scale for determining whether or not quantum features of the
system can survive~\cite{Ved}. The effective temperature can be
much lower than the temperature of the bath $T$ so
as to sustain quantum entanglement even at high temperature
$T$~\cite{Ved}. The works of~\cite{Hsiang2,Hsiang3} reexamine the
above-mentioned model by considering  time-independent
couplings between two oscillators with the same Ohmic
damping parameters, $\gamma_1=\gamma_2$. Additionally  the
temperatures of two baths are set to be different, say $T_1$ and
$T_2$ respectively. The late-time nonequilibrium steady states are
found where the critical temperature below which quantum
entanglement exists turns out not so surprisingly to be $k_B T_{c}
\sim E \sim \Omega_+$ where  $\Omega_+$ is the  higher frequency among two normal modes frequencies. It seems that parametric driving with the
time-dependent coupling between two oscillators is a key mechanism
for sustaining the entanglement in the system at high temperature.
Nevertheless,  in \cite{Boy}, coherence of two mechanical
oscillators coupled to different and uncorrelated baths is
studied, and is found to be enhanced in the case of $\gamma_1 \neq
\gamma_2$. Thus, in this work we plan to extend the works of
\cite{Hsiang2,Hsiang3} by considering the case when $\gamma_1 \neq
\gamma_2$ with the hope to boost the critical temperature for
the entanglement to a higher one as compared with the case of
$\gamma_1=\gamma_2$. Recently, the model above has also been adopted
to successfully explain the experimental demonstration of a novel
effect of heat transfer between two objects driven by quantum
vacuum fluctuations~\cite{Fon}. Theoretic studies of this model on heat transfer between microsystems are also found for example in ~\cite{Meher,Biehs,Xuereb,Asadian}.

Our presentation is organized as follows. In next section, we
introduce the model, and briefly review the idea of open quantum
system with the method of the closed-time-path formalism. The
environmental degrees of freedom in the full density matrix of the
system-plus-environment are traced over to obtain the reduced
density matrix of the system. Environmental effects are then all
encoded in the influence functional, which can be determined by
nonequilibrium two-point correlators. Then the corresponding
Heisenberg-Langevin equations for two oscillators involving the damping as well as noise terms are derived, which can
be solved for the general solutions. In Sec. \ref{sec3}, we
construct the covariance matrix, and substitute the solutions of
the Heisenberg-Langevin equations into the matrix elements. In the
late-time limit, the matrix elements are dominated by
the noise correlations on the oscillators. The separability
criterions are discussed. Violation of the criterions allows us to
compute the critical temperature of the entanglement both
numerically and analytically in Sec. \ref{sec4}. We summarize all
results with their implications in Sec. \ref{sec5}.

\section{The model: two oscillators coupled to its own heat baths}\label{sec2}

We consider the model of two quantum oscillators coupled to their
own heat baths of quantum scalar fields at different temperatures.
The action is described
by~\cite{Hsiang1,Hsiang2,Hsiang3} {\begin{eqnarray} \label{action}
S[ \chi, \varphi] &=& S_{\chi}[\chi_1,\chi_2]+ S_{\varphi}[\varphi_1,\varphi_2]+ S_{\chi\varphi}[\chi_{1,2},\varphi_{1,2}] \nonumber\\
&=& \int \, ds \, \bigg[ \frac{m}{2} (\dot\chi_1)^2 -\frac{m \Omega^2}{2} \chi_1^2 +  \frac{m}{2} (\dot\chi_2)^2 -\frac{m \Omega^2}{2} \chi_2^2  -m\sigma \chi_1(s) \chi_2(s) \bigg] \nonumber\\
&&\quad\quad  + \int d^4 x\, \frac{1}{2} \bigg[ \partial_\mu \varphi_1 \partial^\mu \varphi_1 + \partial_\mu \varphi_2 \partial^\mu \varphi_2 \bigg]\nonumber\\
&&\quad\quad \quad+  g_1 \int d^4 x \, \chi_1 (s)\, \delta^{(3)} ({\bf{x}}- {\bf{z}}_1 (s)) \, \varphi_1(x) \nonumber\\
&&\quad\quad\quad +  g_2 \int d^4 x \, \chi_2 (s)\, \delta^{(3)}
({\bf{x}}- {\bf{z}}_2 (s)) \, \varphi_2(x) \, . \end{eqnarray}} Two
oscillators have the same oscillation frequency $\Omega$ and  mass $m$, and
they couple to each other with a coupling constant $\sigma$.  The
coupling of the oscillator $\chi_{1,2}$ to the heat bath of a
scalar field $\varphi_{1,2}$ has the coupling strength $g_{1,2}$.
Moreover, ${\bf z}_{1,2}$ is the prescribed trajectory of
the oscillators. Here we assume that the initial density matrix
for the whole system (oscillators-plus-fields) at
time $t_i =0$ is factorizable as
   \begin{equation} \rho(0)=\rho_{\chi}(0)
\otimes \rho_{\varphi_1} \otimes \rho_{\varphi_2} \, .
   \end{equation}
The fields are initially in thermal equilibrium at temperature
$\beta_1=1/T_1$ for the field $\varphi_1$ and $\beta_2=1/T_2$ for
the field $\varphi_2$ with $T_1\neq T_2$ in general. Their
respective density matrices are
 given by
\begin{equation}\label{initialcondphi}
    \rho_{\varphi_{1}}=e^{-\beta_1 H[\varphi_1]}/ {\rm Tr} \{ e^{-\beta_1 H[\varphi_1]}  \} \,, \quad\quad \rho_{\varphi_{2}}=e^{-\beta_2 H[\varphi_2]}/ {\rm Tr} \{  e^{-\beta_2 H[\varphi_2]}\} \,,
\end{equation}
where $H [\varphi_{1,2}]$ is the Hamiltonian for the free field
$\varphi_{1,2}$, constructed from $S_\varphi
[\varphi_1,\varphi_2] $ in (\ref{action}). The  density matrix
$\rho (t)$ of the whole system  evolves unitarily according to \begin{equation}
\rho (t) = U(t,0 ) \, \rho (0) \, U^{-1} (t ,0)\,, \end{equation} where $U(t
,0 )$ is the time evolution operator. The effects from the
environment to the system can be summarized in the reduced density
matrix $\rho_r (t)$, which is obtained by tracing out the
environmental degrees of freedom in $\rho (t)$. Here we provide a
brief summary of the main results of the reduced density matrix of
the system, and a mini review of how to obtain the equations of
motion for the position operators of two coupled oscillators with
environmental effects. We start with the reduced density matrix,
expressed as
\begin{align}
&\quad\rho_{\chi}(\chi_{1 F},\chi'_{1 F}, \chi_{2 F},\chi'_{2 F};t) =\int_{-\infty}^{\infty}\!\left\{\prod_{a=1}^{2}d\chi_{a I} d\chi'_{aI}\right\}\;\rho_{\chi}(\chi_{1I},\chi'_{1I},\chi_{2I},\chi'_{2I},0)\nonumber\\
&\quad \left\{\prod_{a=1}^{2}\int_{\chi_{aI}}^{\chi_{aF}}\!\mathcal{D}\chi_{a+}\!\int_{\chi'_{aI}}^{\chi'_{aF}}\!\mathcal{D}\chi_{a-}\right\}\exp\Bigl(i\,S_{\chi}[\chi_{1+}, \chi_{2+}]-i\,S_{\chi}[\chi_{1-},\chi_{2-}]\Bigr)\times \mathcal{F}[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-}] \, .\notag
\end{align}
The influence functional $\mathcal{F}$  can be written in terms of nonequilibrium two-point
correlators constructed from the environment fields as
 \begin{align}
&\quad\mathcal{F}[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-}]
=e^{i\,S_{IF}[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-}]}\notag\\
&\quad\quad
=\prod_{a=1}^{2}\exp\biggl\{\frac{i}{2}\,\int_{0}^{t}\!ds\,ds'\biggl(\Bigl[\chi_{a+}(s)-\chi_{a-}(s)\Bigr]G_{R,\,T_a}(s,s')\Bigl[\chi_{a+}(s')+\chi_{a-}(s')\Bigr]\biggr.\biggr.\notag\\
&\qquad\qquad+\biggl.\biggl.i\,\Bigl[\chi_{a+}(s)-\chi_{a-}(s)\Bigr]G_{H,\,T_{a}}(s,s')\Bigl[\chi_{a+}(s')-\chi_{a-}(s')\Bigr]\biggr)\biggr\}\,,
 \end{align}
where $S_{IF}$ is called the influence action. The retarded
Green's function $G_{R,\,T_a}$ is defined by \begin{equation}
G_{R,\,T_a}(s,s')=i \, g_{a}^2 \,\theta(s-s')\, \Big\langle
\Bigl[\varphi_{a}({\bf z}_{a}(s),s),\varphi_{a}({\bf
z}_{a}(s'),s')\Bigr]\Big\rangle \end{equation} {and the {Hadamard function}
$G_{H,\,T_{a}}$ by} \begin{equation}  G_{H,\,T_{a}}(s,s')=\frac{g_{a}^2}{2}\,
\Big\langle \Bigl\{\varphi_{a}({\bf z}_{a}(s),s),\varphi_{a}({\bf
z}_{a}(s'),s')\Bigr\}\Big\rangle\, \end{equation} with $a=1,2$. Notice that
we have absorbed the coupling constant $g_{a}^2$ into the
definition of the Green's functions. The Hadamard function is
simply the expectation value of the anti-commutator of the quantum
field $\varphi_a$ with respect to the thermal state at temperature
$T_a$, and notice that the retarded Green's function does not have
any temperature dependence due to the linear coupling of the
scalar field to the oscillator. The kernels $G_{H,\,T_{a}}$ and
$G_{R,\,T_a}$ respectively are in turn linked by the
fluctuation-dissipation relation. The fluctuation-dissipation
relation is known to play a pivotal role in balancing these two
effects in order to dynamically stabilize the nonequilibrium
evolution of the system under a fluctuating environment.
Mathematically, it relates the Fourier transform of the
fluctuation kernel  $G_{H,\,T_{a}}$  to the imaginary part of the
retarded kernel $G_{R,\,T_a}$ as follows \begin{eqnarray}
&&G ( s,s')= \int \frac{d \omega }{2\pi} \,G ({\bf z}(s),{\bf z}(s'); \omega) \, e^{-i \omega (s-s')}\,,\nonumber\\
&&G_{H,T_a}({\bf z}(s),{\bf z}(s'); \omega) =
\coth\bigg[\frac{\omega}{2 T_a} \bigg] \,  {\rm Im}
G_{R,\,T_a}({\bf z}(s),{\bf z}(s'); \omega)  \, . \end{eqnarray}

Thus, one can define the coarse-grained effective action as
\begin{equation}
S_{CG}[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-}]  =S_{\chi}[\chi_{1+}, \chi_{2+}]-S_{\chi}[\chi_{1-}, \chi_{2-}]+ S_{IF}[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-}] \,.
\end{equation}
To find the time evolution of  two oscillators, we derive the Heisenberg-Langevin
equations for the quantum operators $\hat\chi_1$ and $\hat\chi_2$ that
incorporate  environmental effects. This can be done
by introducing an auxiliary variable $ \eta_{T_a} (s)$, the noise
force, with a Gaussian distribution function:
\begin{equation}
P[\eta_{T_a} (s)] = \exp \left\{ - \frac{1}{2}  \, \int_{0}^{t} ds
\, \int_{0}^{t} ds' \, \eta_{T_a} (s) \, G^{ -1}_{H ,T_{a}} (s-s') \, \eta_{T_a}
(s') \right\} \, . \label{noisedistri}
\end{equation}
In terms of the noise force $\eta_{T_a} (s) $,  $ S_{CG} $ can be
rewritten as an ensemble average over $ \eta_{T_a} (s)$,
\begin{equation}
\exp i S_{CG}[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-}]  =  \int \!
\prod_{a=1}^{2} \! \mathcal{D}\eta_{T_a} \, P [\eta_{T_a} (s)] \,
\exp i S_{\eta} \left[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-} ;
\eta_1,\eta_2 \right] \, ,
\end{equation}
where the stochastic coarse-grained effective action   $ S_{\eta
}$
is given by
\begin{eqnarray}
&& S_{\eta}\left[\chi_{1+},\chi_{2+},\chi_{1-},\chi_{2-} ; \eta_1,\eta_2 \right]  =S_{\chi}[\chi_{1+}, \chi_{2+}]-S_{\chi}[\chi_{1-}, \chi_{2-}]  \nonumber \\
&& \quad\quad\quad   + \sum_{a=1}^{2} \frac{1}{2}\,\int_{0}^{t}\!ds\,\int_0^t \, ds'\Bigl[\chi_{a+}(s)-\chi_{a-}(s)\Bigr]G_{R,\,T_a}(s,s')\Bigl[\chi_{a+}(s')+\chi_{a-}(s')\Bigr]\biggr.\biggr.\nonumber\\
&& \quad\quad \quad\quad \quad\quad \quad\quad \quad\quad
\quad\quad+  \sum_{a=1}^{2} \int_{0}^{t} ds \, \eta_{T_a} (s)
\Bigl[\chi_{a+}(s)-\chi_{a-}(s)\Bigr]\, . \end{eqnarray} Then, the equations
of motion for $\hat\chi_1$ and $\hat\chi_2$ can be
derived from the action $S_{\eta}$ by introducing the center of mass
coordinate $\chi_{a}$ and the relative coordinate $R_a$, $
    \chi_{a}=\frac{1}{2}\bigl(\chi_{a+}+\chi_{a -}\bigr)\,, R_a=\chi_{a +}-\chi_{a -}\, $,
and then taking the variation of $S_{\eta}$ with respect to $R_a$. For
simplicity, we assume that two oscillators barely move away from the
spatial locations of ${\bf z}_{0 a}$ so that ${\bf z}_a (s) \simeq
{\bf z}_{0 a}$. In this approximation, the retarded Green's
function $G_{R,\,T_a}$ and the Hadamard function $G_{H,\,T_a}$ can
be expressed as \begin{eqnarray}
G_{R,\,T_a}(s,s')&=& -\frac{1}{2\pi} \,g_{a}^2\, \theta(s-s') \, \delta' (s-s')\, , \nonumber\\
G_{H,T_a} (s,s') &=& \frac{g_{a}^2}{4 \pi} \int \frac{ d \omega}{2\pi} \omega \coth \bigg[ \frac{\omega}{2 T_a} \bigg] \, e^{-i \omega (s-s')}\, .
\end{eqnarray}
With the Green's functions above, the Heisenberg-Langevin  equations  for quantum oscillators can be written as
\begin{align}
\ddot{\hat\chi}_1 \, + 2\gamma_{1}\, \dot{\hat\chi}_1+\Omega^2\hat\chi_1+\sigma\hat\chi_2=\frac{\eta_{T_1}}{m}, \label{chi1} \\
\ddot{\hat\chi}_2\, +2\gamma_{2}\, \dot{\hat\chi}_2+\Omega^2\hat\chi_2+\sigma\hat\chi_1=\frac{\eta_{T_2}}{m} \, . \label{chi2}
\end{align}
The effects from the retarded Green's function $G_{R a}$ not only slow down the motion of $\chi$
through the induced damping terms with the damping parameters $\gamma_a=g_a^2/8 \pi m$, but also give a shift to the
oscillation frequency, with $\delta \Omega_a^2=-4 \gamma_a \delta(0)$. Here we consider the weak oscillator-bath couplings with small $g_a$ where the corrections $\delta \Omega_a^2 $ can be ignored as compared with $\Omega^2$.

It worths mentioning that there are two different sources of
fluctuations, over which the averages are taken on  $\hat \chi_1$ and
$\hat\chi_2$. One is the average over intrinsic quantum fluctuations
of the oscillators, and the other is the average over the noise
manifested from thermal fluctuations of the environments. The
distribution function $P[\eta_{T_a}(s)]$ in (\ref{noisedistri})
leads to the correlation function of the noise as follows
\begin{equation} \langle \eta_{T_a} (s) \,  \eta_{T_a} (s') \rangle= G_{H, T_a}
(s-s') \,, \end{equation} where
\begin{align} \label{G_H}
G_{H, T_a}(s-s')= 2 \, m \gamma_{a}\int
\frac{d\omega}{2\pi}\,\omega \coth\bigg[{\frac{\omega}{2
T_a}}\bigg] e^{-i\omega(s-s')} \,.
\end{align}

In~\cite{Boy}, the model of~(\ref{action}) has been considered
where  the environment consists of a collection of harmonic
oscillators. The Heisenberg equations of motion of the system and
the environment can be solved exactly, giving the same form of the
equations in (\ref{chi1}) and (\ref{chi2}) with the Green's
functions constructed out of the harmonic oscillators.  In this
work, we derive the Heisenberg-Langevin equations  from the
influence functional.

 \section{Covariance matrix and separability criterions}\label{sec3}

The initial states of two quantum oscillators are Gaussian wave
packets with the initial conditions on the expectation values of the position operator $\hat\chi_a$
and the momentum operator $\hat p_a= m \dot{\hat\chi}_a$
 as follows}
 \begin{eqnarray}
\langle \hat\chi_a (0) \rangle &=& \langle \hat p_a (0) \rangle=0 \, ,\quad\quad \langle \{ \hat\chi_a (0), \hat p_b (0)\}\rangle=0 \, , \label{ini_cond_1}\\
\langle \{\hat \chi_a (0), \hat \chi_b(0) \}\rangle &=&
\delta_{ab} \, \langle {\hat\chi}^2_a (0) \rangle \, , \quad\quad
\langle \{ \hat p_a (0), \hat p_b(0)\} \rangle= \delta_{ab}\,
\langle {\hat p}^2_a (0) \rangle \, , \label{ini_cond_2}
 \end{eqnarray}
where two oscillators are initially in a separable state. The interaction between two oscillators starts to build up the
entanglement between them.

A Gaussian state is completely characterized by its first and
second statistical moments of a {raw matrix}
defined as ${\bf \hat
X}=(\hat\chi_1,\hat p_1 ,\hat\chi_2,\hat p_2)$,
where the first moments vanish, $\langle {\bf \hat X} \rangle =0 $
due to the chosen initial conditions and the second moments are
specified by the covariance matrix given by
   \begin{equation} {
V}_{ij}=\frac{1}{2} \langle  { \hat X}_i { \hat X}_j + { \hat X}_j
{\hat X}_i \rangle- \langle {\hat X}_i \rangle \langle { \hat
X}_j\rangle \,
  \end{equation}
with $i,j=1,2,3,4$. For any operator $\hat O$,  $\langle \hat O
\rangle={{ \rm Tr} [\rho_\chi \hat O ]}$ where $\rho_{\chi}$ is
{the reduced}
density matric of $\chi_1$ and $\chi_2$. Apparently, ${\bf V}$ is
a real symmetric matrix, namely ${\bf V}={\bf V}^T$. Also, with
the Gaussian states described above, we have
$V_{23}=-V_{14}$,\,\,$V_{31}=V_{13}$,\,\,$V_{32}=-V_{41}$,
\,\,$V_{41}=-V_{14}$,\,\,$V_{42}=V_{24}$ and
$V_{12}=V_{21}=V_{34}=V_{43}=0$ where  the covariance matrix can
be written as
\begin{align}
\mathbf{V}=\begin{pmatrix}
A  & C\\
C^T & B
\end{pmatrix}
\end{align}
with
\begin{align}
A=\begin{pmatrix}
V_{11}& 0\\ 0& V_{22}
\end{pmatrix},\quad
B=\begin{pmatrix}
V_{33}& 0\\ 0& V_{44}
\end{pmatrix},\quad\text{and}\,\,\,
C=\begin{pmatrix}
V_{13}& V_{14}\\ -V_{14}& V_{24}
\end{pmatrix}.
\label{ABC}
\end{align}
Considering the {positive definite} density matrix
$\rho_{\chi}$, Heisenberg uncertainty principles  can be cast in the form
\cite{Simon1,Simon2}
  \begin{equation}
  {\bf V} +i {\bf K} \ge 0 \,  \label{Hei}
  \end{equation}
with the matrix $\bf K$ defined as
 \begin{equation}
 {\bf K}=\begin{pmatrix}
0& 1 &0 & 0\\
-1& 0 &0&0\\
0&0&0&1\\
0&0&-1&0
\end{pmatrix}\,,
 \end{equation}
and should be obeyed by any quantum system. The uncertainty principle  is a
direct consequence of the canonical commutation relation  and the
non-negativity of the density matrix. Moreover {\bf V} can be
diagonalized by the sympletic transformation $S \in Sp(4,R)$, the
ten-parameter real symplectic group, where {two} sympletic
eigenvalues, $\eta_{\lessgtr}$ {(with $\eta_> > \eta_<$)} would
satisfy $\eta_\lessgtr \ge 1/2$ as the result of (\ref{Hei}) and
encode essential information for the Gaussian states~\cite{Simon}. According to \cite{Per,Hor},
one can define the partial transpose $\bar \rho_{\chi}$ of a
bi-particle quantum state $\rho_{\chi}$ as the transpose performed
on  one of two particles in a given basis. Accordingly, the the
partial transpose covariance matrix is denoted as  ${\bf \bar V}$.
Together with the positivity of the partially transposed density
matrix $\bar\rho_{\chi}$, the necessary and sufficient
separability criterion (Peres-Horodecki-Simon (PHS)  criterion)
for {bipartite} continuous Gaussian variable systems
is then expressed as \cite{Simon}
   \begin{equation} {\bf \bar V} +i {\bf K} \ge 0 \, .
   \label{PHS}
   \end{equation}
The violation of the PHS criterion
indicates the existence of quantum entanglement between two Gaussian systems.
Again, the associated {two} sympletic eigenvalues
$\bar \eta_{\lessgtr}$ {of ${\bf \bar V}$}
would satisfy $\bar
\eta_{\lessgtr}\ge 1/2$ due to (\ref{PHS}). The
expressions of $\bar \eta_{\lessgtr}$  in terms of the matrix $A$, $B$, and $C$ defined above
will be discussed below as a measure of quantum entanglement of
the Gaussian states in this study.

To find the covariance matrix we need to solve Eqs.(\ref{chi1})
and (\ref{chi2}) where the general solutions are the sum of the
homogeneous solution $\chi_{a;h}$  that depends on the initial
conditions, $\chi_a (0)$ and $\dot\chi_a (0)$, and the particular
solution $\chi_{a;p}$ that satisfies the full equations with the
noise. Let us write the time dependence of $\chi_{a;h}  $ as
$\chi_{a;h} (t) \propto e^{-i \bar{\Omega}_{a,\pm} t}$.  The frequency
$\bar{\Omega}_{a,\pm}$ is determined by the equation, $\tilde{\bf
D}^{-1} (\bar{\Omega}_{a,\,\pm })=0$ with the matrix $\tilde{\bf D}
(\omega)$ defined as
\begin{align}\label{tildeD}
\tilde{\bf D}(\omega)&=\frac{1}{-\omega^2\mathbf{I}+\mathbf{\Omega}^2-i2\omega\mathbf{\Gamma}}\,,
\end{align}
where
\begin{align}
&\mathbf{I}=\begin{pmatrix}
1 & 0 \\
0 & 1
\end{pmatrix},\quad
\mathbf{\Omega}^2=\begin{pmatrix}
\Omega^2 & \sigma \\
\sigma & \Omega^2
\end{pmatrix},\quad
\mathbf{\Gamma}=\begin{pmatrix}
\gamma_1 & 0 \\
0 & \gamma_2
\end{pmatrix}\, .
\end{align}
This gives the following determinant,
\begin{equation}
\det\tilde{D}^{-1}(\omega)=\left[(-\omega^2+\Omega^2-i2\omega\gamma_{1})(-\omega^2+\Omega^2-i2\omega\gamma_{2})-\sigma^2\right].
 \end{equation}
Solving $\tilde{\bf D}^{-1} (\bar{\Omega}_{a,\,\pm})=0$, we find
\begin{eqnarray}
&&\bar{\Omega}_{1,\pm}\simeq\Omega_+\pm\frac{i}{2}(\gamma_1+\gamma_2),\\
&&\bar{\Omega}_{2,\pm}\simeq\Omega_-\pm\frac{i}{2}(\gamma_1+\gamma_2),\label{freq}
\end{eqnarray}
with $\Omega_+\equiv\sqrt{\Omega^2+\sigma}$, $\Omega_-\equiv\sqrt{\Omega^2-\sigma}$.

We consider that  two oscillators undergo underdamped oscillations
{in the case of $\Omega^2 > \sigma$ and also both
$\Omega$ and  $\sqrt{\sigma}$ being much larger than $\gamma_1$ and
$\gamma_2$.} Asymptotically as $t \rightarrow \infty$, the
homogeneous solution $\chi_{a;h}$  damps out exponentially and
its contributions to the
covariance matrix with the initial condition dependence can be ignored. Thus, the late-time behavior of
the covariance matrix is determined by a
{particular} solution $\chi_{a;p}$ due to the noise terms $\eta_{T_a}$, which then lead to the
following non-vanishing elements
\begin{align}
 V_{11}&=\frac{1}{2}\langle{\chi_1(\infty),\chi_1(\infty)}\rangle\nonumber\\
 &=\frac{1}{m^2}\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\left(\lvert\tilde{D}_{11}(\omega)\, \rvert^2 \, \tilde{G}_{H,T_1}(\omega)\, +\lvert\tilde{D}_{12}(\omega)\rvert^2\, \tilde{G}_{H,{T_2}}(\omega)\right),\label{v_11}\\
  V_{22}&=\frac{1}{2}\langle{p_1(\infty),p_1(\infty)}\rangle\nonumber\\
 &=\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\,\omega^2\, \left(\lvert\tilde{D}_{11}(\omega)\rvert^2\, \tilde{G}_{H, {T_1}}(\omega)\, +\lvert\tilde{D}_{12}(\omega)\rvert^2\, \tilde{G}_{H, {T_2}}(\omega)\right),\label{v_22}\\
  V_{33}&=\frac{1}{2}\langle{\chi_2(\infty),\chi_2(\infty)}\rangle\nonumber\\
 &=\frac{1}{m^2}\int_{-\infty}^{\infty}\frac{d\omega}{2\pi} \, \left(\lvert\tilde{D}_{21}(\omega)\rvert^2\, \tilde{G}_{H,{T_1}}(\omega)\, +\lvert\tilde{D}_{22}(\omega)\rvert^2\, \tilde{G}_{H,{T_2}}(\omega)\right),\label{v_33}\\
  V_{44}&=\frac{1}{2}\langle{p_2(\infty),p_2(\infty)}\rangle\nonumber\\
 &=\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\,\omega^2 \, \left(\lvert\tilde{D}_{21}(\omega)\rvert^2\, \tilde{G}_{H,{T_1}}(\omega)\, +\lvert\tilde{D}_{22}(\omega)\rvert^2\, \tilde{G}_{H,{T_2}}(\omega)\right),\label{v_44}\\
  V_{13}&=\frac{1}{2}\langle{\chi_1(\infty),\chi_2(\infty)}\rangle\nonumber\\
 &=\frac{1}{m^2}\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\,
 \left(\tilde{D}_{11}^*(\omega)\tilde{D}_{21}(\omega)\, \tilde{G}_{H,{T_1}}(\omega)\, +\tilde{D}_{12}^*(\omega)\tilde{D}_{22}(\omega)\, \tilde{G}_{H,{T_2}}(\omega)\right),\label{v_13}\\
 V_{14}&=\frac{1}{2}\langle{\chi_1(\infty),p_2(\infty)}\rangle\nonumber\\
 &=\frac{-i}{m}\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\,\omega\,
 \left(\tilde{D}_{11}^*(\omega)\tilde{D}_{21}(\omega)\, \tilde{G}_{H,{T_1}}(\omega)\, +\tilde{D}_{12}^*(\omega)\tilde{D}_{22}(\omega)\, \tilde{G}_{H,{T_2}}(\omega)\right),\label{v_14}\\
  V_{24}&=\frac{1}{2}\langle{p_1(\infty),p_2(\infty)}\rangle\nonumber\\
 &=\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\,\omega^2\, \left(\tilde{D}_{11}^*(\omega)\tilde{D}_{21}(\omega)\,
 \tilde{G}_{H,{T_1}}(\omega)\, +\tilde{D}_{12}^*(\omega)\tilde{D}_{22}(\omega)\, \tilde{G}_{H,{T_2}}(\omega)\right)\,\label{v_24} .
\end{align}

In the case of continuous Gaussian variables, it has been shown
that PHS separability criterion in (\ref{PHS}) in quantum systems
 {together with
the} Heisenberg uncertainty relation in (\ref{Hei}) is equivalent
to the following
{inequalities, expressed} in terms of the $Sp(2,R)
\otimes Sp(2,R)$ invariants constructed out of the matrices
$A$,$B$, and $C$ in~(\ref{ABC}) as~\cite{Simon}
\begin{align}
\zeta_\pm=\det{A}\cdot\det{B}-\text{Tr}(A\cdot J\cdot C\cdot J\cdot B\cdot J \cdot C^T\cdot J)-\frac{1}{4}(\det A+\det B) +(\det C \pm\frac{1}{4})^2 \ge 0 \, . \label{zeta_pm}
\end{align}
where the matrix $J$ is defined to be
\begin{align}
J=\begin{pmatrix} 0 & 1\\ -1& 0
\end{pmatrix}\, .
\end{align}
In this form, the condition for $\zeta_-$ is the Heisenberg
uncertainty relation while the condition for $\zeta_+$ is the PHS
criterion, as can be noticed from (\ref{Hei}) and (\ref{PHS}).  In
fact, the change from the density matrix $\rho_{\chi}$ to the
partial transposed density matrix $\bar \rho_{\chi}$ gives the
sign flip in $\det C$. Because $\zeta_+=\zeta_-+ \det C$, the
assumption that the uncertainty relation, $\zeta_-\ge0$ always
true leads to $\zeta_+\ge 0$ when $\det C>0$. For $\det C<0$, the
possibility of $\zeta_+ <0$ implies the  existence of quantum
entanglement~\cite{Simon}. So, the condition, $\det
C=V_{13}V_{24}+V_{14}^2<0$, indicates the possible existence of
quantum entanglement in the {bipartite} Gaussian states, which highlights the
importance of cross-correlations on the entanglements, giving
$\zeta_+ <0$.

Once we have the covariance matrix for the coupled
oscillators in  nonequilibrium steady states, we
 construct $\zeta_+$ according to (\ref{zeta_pm})
\cite{Hsiang2,Hsiang3}. In fact,  ${\bf
\bar V}$ can be diagonalized by the sympletic transformation $S
\in Sp(4,R)$. In particular, the sympletic eigenvalues of partial
transport ${\bf \bar V}$ are
\begin{align}\label{eta_gl}
\bar \eta_{\lessgtr}=\left[\frac{\bar\Delta}{2}\pm \sqrt{\ \frac{\bar \Delta^2}{4}-\det V}\,\,
\right]^{1/2}
\end{align}
where $\bar\Delta =\det A+\det B-2 \det C$.
 Moreover, inequality
(\ref{PHS}) can be recast as a constraint  $\bar \Delta \le
\frac{1}{4}+ 4 \det V $, leading to $ (\bar\eta^2_<
-\frac{1}{4})(\bar\eta^2_>-\frac{1}{4}) \ge 0$. Assuming $\bar
\eta_> >\bar \eta_<$, the PHS separability criterion then simply
reads
  \begin{equation}
  \label{PHS1}
  \bar \eta_< \ge \frac{1}{2} \,.
  \end{equation}
Violating the separability criterion, namely $\bar \eta_< <
\frac{1}{2}$, can serve as a measure for the entanglement that we
will focus on in this paper. {It has also been suggested that
negativity~\cite{Vid} and logarithmic negativity~\cite{Ple}, which
are defined respectively as,
 \begin{equation}
 N(\rho)=\max\{0,\frac{1-\bar \eta_<}{2\bar \eta_<}\},~~E(\rho)=\max\{0,-\ln 2\bar \eta_<\}
 \end{equation}
are good entanglement measures. In particular, they do not increase
on average under various local quantum operations. The roles of
these entanglement measures in our setup deserve further study.}

\section{Numerical/analytical analysis of quantum entanglement}\label{sec4}

Violation of the separability criterions, namely $\zeta_{+} < 0$
and $\bar\eta_< < 1/2$,  indicates the existence of quantum
entanglement of the systems. We now numerically compute $\zeta_+$
and $\bar \eta_{<}$ in~(\ref{zeta_pm}) and (\ref{eta_gl})
respectively to examine their behaviors, which are shown in
Fig.~\ref{zeta_eta}. For a given value $\Omega$, $\sigma$
($\Omega^2 >\sigma$), $\gamma_1$ and $\gamma_2$, and also for a
fixed $\beta_2$, we depict $\zeta_+$ and $\bar \eta_{<}-1/2$ as a
function of $\beta_1$. We find {the} critical value $\beta_{1c}$
obtained from $\zeta_+ = 0$ and $\bar \eta_{<}= 1/2$, above which
($\beta_1 \ge \beta_{1c}$) quantum entanglement exists. In the
range of $\beta_1 \ge \beta_{1c}$, we see that $\bar \eta_{<}$ is
a monotonically decreasing function of $\beta_1$  whereas $\zeta_+
$ is not. It is known that $\bar \eta_{<}$  can serve as a
sensible measure as quantifying the degree of the entanglement
through { negativity and logarithmic negativity for example.}
Fig.~\ref{critical_T} shows the line of the critical values of
$\beta_{1c}$ and $\beta_{2c}$. In the left-panel we choose
$\gamma_1=\gamma_2$, and in the right-panel,$\gamma_1 < \gamma_2$.
In the regime of $\beta_{2c} > \beta_{1c}$ and for the same
$\beta_{2c}$, the corresponding $\beta_{1c}$ given by this
critical temperature line in the case of  $\gamma_1 < \gamma_2$
(right-panel) changes to a much smaller value  than that in the
case of $\gamma_1=\gamma_2$ (left-panel). Nevertheless, for
$\beta_{1c} > \beta_{2c}$, and for the same $\beta_{1c}$, the
value of $\beta_{2c}$  in the case of $\gamma_1 < \gamma_2$
(right-panel) becomes larger  than that in the case
$\gamma_1=\gamma_2$ (left-panel). Thus, the difference between
$\gamma_1$ and $\gamma_2$ ($ \gamma_1 <\gamma_2$) can push the
critical temperature in the bath 1 ($T_{1c}=1/\beta_{1c}$) to a
higher temperature for a fixed $\beta_{2c}$ in the regime
$\beta_{2c}>\beta_{1c}$ whereas it also pulls the critical
temperature ($T_{2c}=1/\beta_{2c}$) in the bath 2 down to a lower
value for a fixed $\beta_{1c}$ in the regime $\beta_{1c} >
\beta_{2c}$. This is one of our main results in this paper to be
further studied analytically in below.
\begin{figure}[h]
\centering
\includegraphics[scale=1]
{fig1.eps} \caption{The separability criterions are all dimensionless and
 depend on  dimensional variables given with respect to some relevant unit of, say $\Omega_0$.
 Thus, the criterions $\zeta_{+}$ (thick
solid line) and $\bar\eta_{<}-1/2$ (thin solid line) are plotted as the function of $\beta_1$ in the unit of $1/\Omega_0$ by fixing $\beta_2=1.5/ \Omega_0$, and  the parameters
$\Omega=5 \Omega_0$, and $\sigma=24 \Omega_0^2$, $\gamma_1=0.005 \Omega_0$, and $\gamma_2=0.25 \Omega_0$
according to the exactly numerical results obtained from (\ref{zeta_pm}) and (\ref{eta_gl})
respectively in that the momentum integration has logarithmic
divergence to be cut off by the chosen cutoff scale $\Lambda=5000\Omega_0$. The approximate
results for $\zeta_{+}$ (blue dotted line) and $\bar\eta_{<}-1/2$ (red
dotted line) are also plotted by substituting  analytically approximate
expressions of  the covariance matrix elements in
(\ref{V_11})-(\ref{V_24}) to (\ref{zeta_pm}) and (\ref{eta_gl}).
We see a  good agreement between the exact and approximate results
in the  parameter regime of validity of the approximations, namely $\beta_1 \Omega_+ \ll1$ and $\beta_2 \Omega_- \gg1$  with $\Omega_+\simeq 7 \Omega_0$ and $\Omega_-\simeq1 \Omega_0$}.
\label{zeta_eta}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[scale=1.0]
{fig2.eps} \caption{The line of the critical values of
$\beta_{1c}$ and $\beta_{2c}$ in the unit of $1/\Omega_0$ (black solid line) exactly determined by the
sympletic eigenvalue $\eta_<=1/2$ in (\ref{eta_gl}) and obtained numerically
 is drawn for  $\gamma_1=\gamma_2=0.25\Omega_0$ (left-panel) and  for $\gamma_1=0.005\Omega_0,\,\gamma_2=0.25\Omega_0$ (right-panel) as a comparison where the parameters $\Omega$ and $\sigma$ remain the same as in Fig.~\ref{zeta_eta}. The critical value line  (red dotted line) is also drawn with the same parameters above, but is determined by substituting the approximate  covariance matrix elements in (\ref{V_11})-(\ref{V_24}) into (\ref{eta_gl}), which also show a good agreement with the exact results in the regime of $\beta_1 \Omega_+ \ll1$, $\beta_2 \Omega_- \gg1$  with $\Omega_+\simeq 7 \Omega_0$ and $\Omega_-\simeq1 \Omega_0$}.\label{critical_T}
\end{figure}

In this two oscillators system, two real parts of (\ref{freq}) are $\Omega_+$ and $\Omega_-$ with $\Omega_+ > \Omega_-$ for $\sigma>0$.
To find the analytical expression for the critical temperatures,
we approximate the covariance matrix elements by considering the high-T limit $\beta_1 \Omega_{+} \ll1$
with reference to the higher frequency mode in the bath 1 and the low-T limit  $\beta_2\Omega_{-} \gg1$
with reference to the lower frequency mode instead in the bath 2, and also
$\gamma_a \ll \Omega_{\pm}$ in the weak damping limit.
Retaining the terms at the relevant order they are summarized as
\begin{align}
&V_{11}=V_{33}\nonumber\\
&\quad\,\,=\frac{1}{m}\left(\frac{\Omega^2}{\Omega_+^2\Omega_-^2}\right)\frac{ \gamma_1}{(\gamma_1+\gamma_2)}\frac{1}{ \beta_1 }+{
\frac{\gamma _2}{4m \left(\gamma _1+\gamma _2\right)} \left(\frac{1}{\Omega_+}+\frac{1}{\Omega_-}\right)}+\frac{\gamma_2}{2\pi m\sigma}\ln \left(\frac{\Omega_+}{\Omega_-}\right)
\nonumber\\
&\quad\quad \,\,-\frac{\gamma _2}{2 \pi  m}\left(\frac{\Omega^2}{\Omega_+^2\Omega_-^2}\right)+\frac{2 \pi  \gamma _2 \sigma ^2}{ 3m{\Omega_+^4\Omega_-^4}}\frac{1}{\beta _2^2}+\mathcal{O}(\gamma_a^2), \label{V_11}
\\[11pt]
&V_{22}=\frac{\gamma_{1}m}{\pi} \ln (\beta_1 \Lambda )\, \Theta (\beta_1 \Lambda -1)+ \frac{m\gamma_1}{(\gamma_1+\gamma_2)}\frac{1}{\beta_1}+{\frac{m\gamma _2}{4 \left(\gamma _1+\gamma _2\right)}\left(\Omega_++\Omega_-\right)}-\frac{m\gamma_2}{2\pi}\nonumber\\
&\quad\qquad+\frac{m\gamma_2\Omega^2}{2\pi\sigma}\ln \left(\frac{\Omega_+}{\Omega_-}\right)+\frac{4 \pi ^3m \gamma _2 \sigma ^2}{15 \Omega_+^4\Omega_-^4}\frac{1}{\beta _2^4}+\mathcal{O}(\gamma_a^2), \label{V_22}
\\[11pt]
&V_{44}=\frac{m\gamma_{1}}{\pi} \ln (\beta_1 \Lambda )\,\Theta (\beta_1 \Lambda -1)+ \frac{m\gamma_1}{(\gamma_1+\gamma_2)}\frac{1}{\beta_1}+\frac{2m\gamma_2}{\pi}\ln\left({\frac{\Lambda}{\Omega_+\Omega_-}}\right)+{\frac{m\gamma _2}{4 \left(\gamma _1+\gamma _2\right)}\left(\Omega_++\Omega_-\right)}\nonumber\\
&\quad\qquad+\frac{m\gamma_2\Omega^2}{2\pi\sigma}\ln \left(\frac{\Omega_+}{\Omega_-}\right)-\frac{m\gamma_2}{2\pi}+\frac{4 \pi ^3m \gamma _2 \sigma ^2}{15 \Omega_+^4\Omega_-^4}\frac{1}{\beta _2^4 }+\mathcal{O}(\gamma_a^2), \label{V_44}
\\[11pt]
&V_{13}=-\frac{1}{m}\left(\frac{\sigma}{\Omega_+^2\Omega_-^2}\right)\frac{\gamma_1}{(\gamma_1+\gamma_2)}\frac{1}{\beta_1}+\frac{\gamma _2  }{4 m\left(\gamma _1+\gamma _2\right)}\left(\frac{1}{\Omega_+}-\frac{1}{\Omega_-}\right)+\frac{\gamma_2 }{2\pi m}\left(\frac{\sigma}{\Omega_+^2\Omega_-^2}\right)\nonumber\\
&\quad\qquad-\frac{2 \pi  \gamma_2 \sigma  \Omega ^2}{3 m\Omega_+^4\Omega_-^4}\frac{1}{\beta _2^2 }+\mathcal{O}(\gamma_a^2),\label{V_13} \\[11pt]
&V_{14}=-\left(\frac{2}{\sigma}\right)\frac{\gamma_1 \gamma_2}{ (\gamma_1+\gamma_2) }\frac{1}{\beta_1}+\frac{8 \pi ^3 \gamma _1 \gamma _2 \sigma }{15 \Omega_+^4\Omega_-^4}\frac{1}{\beta _2^4}+\mathcal{O}(\gamma_a^3),\label{V_14}\\[11pt]
&V_{24}=\left(\frac{m\sigma}{12}\right)\frac{  \gamma_1\beta_1 }{\gamma_1+\gamma_2}+\frac{m\gamma _2 }{4 \left(\gamma _1+\gamma _2\right)}\left(\Omega_+-\Omega_-\right)-\frac{m\gamma_2}{2 \pi}\ln \left(\frac{\Omega_+}{\Omega_-}\right)-\frac{4 \pi ^3 m\gamma _2 \sigma  \Omega ^2}{15 \Omega_+^4\Omega_-^4}\frac{1}{\beta _2^4}+\mathcal{O}(\gamma_a^2). \label{V_24}
\end{align}
\begingroup
Substituting the analytical approximate expressions to
(\ref{zeta_pm}) and (\ref{eta_gl}), we can then compare the approximate results of $\zeta_{+}$
and $\bar\eta_< $ with
their exact numerical ones as shown in Fig.~\ref{zeta_eta},
where the critical value of $\beta_{1c}$ can be correctly obtained
in the case of $\beta_{1c }\Omega_{-} \ll1$ by choosing $\beta_{2c}
\Omega_+ \gg1$ within the  parameter regime where the approximate expressions
are valid. The line of the critical values, $\beta_{1c}$ and
$\beta_{2c}$, resulting from the approximate results are also shown in
Fig.~\ref{critical_T}, which provide a good analytical estimate on
$\beta_{1c}$ and $\beta_{2c}$  again in the regime of $\beta_{1c}
\Omega_{+} \ll1$, $\beta_{2c} \Omega_{-} \gg1$. Substituting
(\ref{V_11})-(\ref{V_24}) into (\ref{zeta_pm}) and (\ref{eta_gl}),
the condition $\bar{\eta}_{<}=1/2$ in the PHS criterion determines
the line of the critical values analytically. To obtain the
analytical expression for the critical temperatures needs further
approximations. Considering the temperature-dependent parts in
(\ref{V_11})-(\ref{V_24}), in the case $\beta_{1c} \Omega_{+} \ll1$,
$\beta_{2c} \Omega_{-} \gg1$, the terms of $1/\beta_2^2$,
$1/\beta_2^4$, and $\beta_1$ are relatively small and thus can be
safely dropped out.  Thus, we consider the  $1/\beta_1$
dependence only.
As for the temperature-independent parts, in the limits of
$\gamma_1 \ll \gamma_2$ and $\gamma_1, \gamma_2 \ll \Omega_{\pm}$,   the
terms proportional to $\gamma$ are ignorably  small except for the
cut-off dependent contributions where the cutoff scale is chosen to be
$\Lambda \gg \Omega$. The PHS criterion then gives
\begin{align}
\beta_{1c} \simeq & 4\pi\gamma_1\bigg/\bigg\{\Big[\pi^2\left(4\gamma_1^2\Omega_+^2+8\gamma_1\gamma_2\Omega_+^2+\gamma_2^2(5\Omega_+^2-2\Omega_+\Omega_-+\Omega_-^2)\right)+\nonumber\\
&\gamma_2^2(\gamma_1+\gamma_2)\ln{\Big\vert\Lambda^4/\Omega_-^4\Big\vert}\left(2\pi(\Omega_--\Omega_+)+(\gamma_1+\gamma_2)\ln{\Big\vert\Lambda^4/\Omega_-^4\Big\vert}\right)\bigg]^{1/2}\nonumber\\
&-\gamma_2(\gamma_1+\gamma_2)\ln{\Big\vert\Lambda^4/\Omega_-^4\Big\vert}-\pi\gamma_2(\Omega_++\Omega_-)\bigg\}, \nonumber\\
\simeq & \frac{4\pi\gamma_1}{\gamma_2\left[\pi\sqrt{5\Omega_+^2-2\Omega_+\Omega_-+\Omega_-^2}-\pi(\Omega_++\Omega_-)-\gamma_2\ln{\Big\vert\Lambda^4/\Omega_-^4\Big\vert}\right]} +\mathcal{O}(\gamma_1^2).
\label{beta1c}
\end{align}
Also, notice that
to be consistent with the small $\gamma$ approximation, the
choice of the cutoff scale is such that the contributions from the
$\ln \Lambda$ dependence are sub-leading as compared with the
leading order terms given by  $\Omega$ and $\sigma$ in~({\ref{beta1c}). The
solution of   $\beta_{1c}$  is found to be $\beta_{1c} \propto
\gamma_1/\gamma_2$ for $\gamma_1 < \gamma_2$ where $\beta_{1c}$ is
significantly suppressed by the smallness of $\gamma_1$ so that
the associated critical temperature $T_{1c}=1/\beta_{1c}$ is boosted into
the hight-$T$ regime with $T_{1c}/\Omega_{+} \gg 1$ with respect to the higher frequency $\Omega_+$ of the normal mode.  On the contrary, in the
regime $\beta_{1c} > \beta_{2c} $, although in Fig.~\ref{critical_T},
$\beta_{2c}$ is not within high-$T$ regime, roughly speaking we expect
$\beta_{2c}$ is given by (\ref{beta1c}) by the replacement of
$\gamma_1 \leftrightarrow \gamma_2$  for $\beta_{1c}$ being a large
value. Thus, for the same $\beta_{1c}$, $\beta_{2c}$ increases  as
$\gamma_1$ decreases from $\gamma_1=\gamma_2$ to $\gamma_1 < \gamma_2$ with a fixed $\gamma_2$ being consistent with the numerical results shown in Fig.~\ref{critical_T}.
In the case of $\gamma_1=\gamma_2$, both $\beta_{1c}$ and
$\beta_{2c}  \propto \mathcal{O}(1/\Omega_+)$ reduces to the findings
in \cite{Hsiang3}. Although the effects
from  the different damping parameters $\gamma_1 \neq \gamma_2$
can push one of the critical temperatures to a higher one, it
may not be so robust to boost the critical temperatures in
both baths to the one higher than the oscillator frequency as in
the case via parametric driving due to the time-dependent
mutual interaction between two oscillators. Our results are consistent with the main conclusion in \cite{Boy} that the large temperature difference in $T_1=1/\beta_1$ and $T_2=1/\beta_2$ in the case of nondegenerate normal modes ($\Omega_+\neq \Omega_-$) can produce the nonvanishing steady-state coherence in high-$T$ limits. And we furthermore show the line of the critical values of $T_{1c}$ and $T_{2c}$ below which the entanglement can survive.
Here we carry out more complete calculations with as few approximation as possible, with which to explore how to achieve hot entanglement between two oscillators.

\section{Comparison to the systems with respective temperature-dependent damping parameters from heat baths}
In this section we  consider the damping
parameter that has the
temperature dependence, say $\gamma_{a T} = \bar\gamma_a T^{\alpha}$ with
$\alpha >0$, resulting from the fact that the system-bath coupling
term is beyond the linear dependence of the bath's
variable.
 In \cite{Lee1,Lee2,Lee3}, we  study the nonequilibrium dynamics of the mirror with
perfect reflection moving in a quantum field.
 The force acting
on the mirror is the radiation pressure of the environmental
field given by  the area integral of the stress tensor, which is quadratic in field variables.
For the system of the $2$-dimensional mirror influenced by a heat bath of free relativistic
scalar fields, the temperature-dependent damping parameters are obtained giving $\alpha=4$.
Later, our studies are extended to  the case of $n$-dimensional mirrors interacting with  a heat bath of Lifshitz scalar fields  with a dynamic exponent
$z$, which are of strongly coupled quantum fields.  The corresponding $\alpha$ using the holographic approach can be computed to be $\alpha=(n+2)/z$.
Taking the strongly self-coupling effects into account, the value of $\alpha$ can even be a fractional number.
With the direct replacement of $\gamma_a \rightarrow \gamma_{aT}=\bar\gamma_a T_a^{\alpha}$ in the Hadamard function $G_{H, T_a}$ (\ref{G_H}) and the matrix $\tilde D$ (\ref{tildeD}), we can numerically calculate the elements of the matrix $V$ from (\ref{v_11})-(\ref{v_24}). Then, from them  the line of the critical values of
$\beta_{1c}$ and $\beta_{2c}$ can be determined by the criterion $\bar{\eta}_{<}=1/2$ in (\ref{eta_gl}), which are shown in Fig.(\ref{fig3}) by choosing the different values of $\alpha$.
In the left-panel (right-panel) of the figure, $\bar \gamma_1 = \bar \gamma_2$ ($\bar \gamma_1 < \bar\gamma_2$) is chosen together with the same values of $\Omega_0$ and $\sigma$ as in Fig.(\ref{zeta_eta}). As $\alpha$ increases while keeping the same $\beta_{2c}$, the corresponding $\beta_{1c}$ increases.
This feature can be  understood  qualitatively from (\ref{beta1c}) for $\beta_{2c} \Omega_- \gg 1$, although the values of $\beta_{1c}$ ($\beta_{1c}\Omega_+ \ge 1$) are beyond the validity of the approximations to achieve it.
With $\gamma_{2T}=\bar\gamma_2/\beta_2^{\alpha}$, as $\alpha$ ($\alpha>0$) increases, for $\beta_{2c} \Omega_- \gg 1$  $\gamma_{2T}$ becomes smaller, leading to the larger values of $\beta_{1c}$.
 In particular, for $\bar \gamma_{2} > \bar\gamma_{1}$, the critical temperature $T_{1c}$ can be boosted into a higher value seen in the right-panel of the figure, which can be qualitatively understandable also from  (\ref{beta1c}) with $\beta_{1c} \propto (\bar \gamma_1/\bar \gamma_2)^{\frac{1}{1+\alpha}}$. {Even for the different $\alpha_a$, namely $\alpha_1\neq \alpha_2$ for the bath 1 and the bath 2, $\beta_{1c} \propto (\bar \gamma_1/\bar \gamma_2)^{\frac{1}{1+\alpha_1}}$.
 \begin{figure}[t]
\centering
\includegraphics[scale=0.6]
{fig3.eps} \caption{The line of the critical values of
$\beta_{1c}$ and $\beta_{2c}$ in the unit of $1/\Omega_0$ exactly determined by $\eta_<=1/2$ in (\ref{eta_gl}) with $ \alpha = 0$ (solid), $\alpha = 1/2$
(dashed), $\alpha  = 1$ (dotted) and $\alpha = 2$ (dash-dotted). The values of $\bar\gamma_a$ are chosen to be
$\bar\gamma_{1T}=\bar\gamma_{2T}=0.25\Omega_0^{1-\alpha}$ (left-panel) and  $\bar\gamma_{1T}=0.005\Omega_0^{1-\alpha},\,\bar\gamma_{2T}=0.25\Omega_0^{1-\alpha}$ (right-panel). The parameters $\Omega$ and $\sigma$ remain the same as in Fig.~\ref{zeta_eta}.}\label{fig3}
\end{figure}
 Thus, the suppression of $\beta_{1c}$ is the most significant when $\alpha=0$ also seen in the figure.
Similar behavior of $\beta_{2c}$ for the same $\beta_{1c}$ can also be interpreted from (\ref{beta1c}) by the
exchange of the subscripts $1\leftrightarrow 2$. Thus, in this model, we find that the systems, which couple to heat baths with the temperature independent damping parameters, are more probable to establish hot entanglement by the mutual interaction as compared with the situations with temperature-dependent damping parameters.

\section{Summaries and looking ahead}\label{sec5}

The main goal of this work is to study the entanglement of quantum
systems at finite temperature. We reconsider the model of two
quantum oscillators coupled to its own environment fields through
the coupling linear in the field variable at different temperatures $T_1$ and $T_2$. By
tracing out the environmental degrees of freedom exactly, the
stochastic effective action is obtained, from which the
Heisenberg-Langevin equations for  two
oscillators are derived including the damping effects of the ohmic form  with the
general damping parameters, $\gamma_1 \neq \gamma_2$  as well as
the noise terms where they obey the fluctuation-dissipation relations. Solving the equations for the general solutions allows us
to compute the position and the momentum uncertainties as well as
the expectation values of position-momentum cross correlations of
the system with the given initially separable Gaussian states of
two oscillators. The interaction between two oscillators
start to build up the entanglement between them.  In the weak
damping limit, the late-time behavior of the system is reached by
the nonequilibrium steady state. The separability criterions
constructed by the covariance matrix elements are computed
numerically and analytically. Violation of the  criterions
implies the existence of the entanglement where the
line of the critical temperature can be determined. Considering $\gamma_1
<\gamma_2$, the critical temperature of $T_{1c}$ can be as high as
$T_{1c}/\Omega_+ \propto \gamma_2/\gamma_1$ with reference  to the higher frequency of the normal mode.
 So, we can
have $T_{1c} \gg \Omega_+$ particularly for $\gamma_1 \ll \gamma_2$,
while keeping $T_{2c} \propto \Omega_+$.  This interesting finding
can be compared with the case of $\gamma_1=\gamma_2$ where both
$T_{1c}$ and $T_{2c}$ are found to be the order of $\Omega_+$. Thus, the effects
from  the different damping parameters $\gamma_1 \neq \gamma_2$
can push one of the critical temperatures to a higher one. This might give the possibility of hot entanglement.
Nevertheless, this
may not be so effective to boost the critical temperatures for
both baths as in the case via parametric driving due to the time-dependent interaction between two oscillators. Also we consider the systems with the temperature-dependent damping parameters of the form $\gamma_{a T} = \bar\gamma_a T^{\alpha}$ ($\alpha >0$), which can obtained by coupling to environment fields at finite temperature  via the area integral
of the stress tensor of the field variables. We find that the boost of the critical temperature to a higher value is more noticeable in the case of $\alpha=0$. These findings deserve
further experimental justification. Finally, it might deserve a further study on parametrically driven, dissipative harmonic oscillators with different damping parameters for more exploration on hot entanglement, as an extension of the work in \cite{Gal}.

\section*{Acknowledgments}
 This work was supported in part by the
Ministry of Science and Technology, Taiwan. We are so grateful to  Jen-Tsung Hsiang for illuminating discussions.

\section*{References}
\bibliographystyle{iopart-num}

redpajama_set_name: RedPajamaArXiv


text:
George Foster Peabody (1852-1938)
Sheila Devaney, University of Georgia,
Business Career
Philanthropy and Politics
George Foster Peabody, noted banker and businessman, left his mark on American society through his philanthropic work. He was born on July 27, 1852, in Columbus, the oldest of four children born to native New Englanders Elvira and George Henry Peabody. Peabody's father had relocated the family from Connecticut to Columbus, where he ran a general store. Growing up in Columbus, Peabody attended private school and later studied at Deer Hill Institute in Danbury, Connecticut. The Civil War (1861-65) pushed the family into poverty, and by 1866 they had relocated to Brooklyn, New York, where the fourteen-year-old Peabody took a job with a wholesale dry goods firm.
George Foster Peabody
mercantile business proved to be a good choice for Peabody. He joined the Reformed Church of Brooklyn Heights, where he met investment banker Spencer Trask, who became not only a good friend but a business partner as well. In 1881 Peabody became a partner in Trask's new investment firm, Spencer Trask and Company. During the 1880s and 1890s the company began to work in several lucrative fields, including electrical construction financing and railroad construction in the western United States. Peabody ran most of the company's railroad investments. Cognizant of such undesirable business practices as rate wars, which were beginning to proliferate in the railroad industry, Peabody advocated government ownership of railroads, and he believed regulation could be the first step in correcting these practices.
After Peabody joined the Episcopal Church in 1880, he became concerned with promoting education
Peabody, Hodgson, Barrow
both within the church and in the South. He was a member of the board of trustees for the American Church Institute for Negroes, which funded Episcopal schools in the South; the Penn Normal Industrial and Agricultural School in St. Helena, South Carolina; Hampton Institute in Hampton, Virginia; Tuskegee Institute in Tuskegee, Alabama; and the University of Georgia in Athens. Peabody gave money for new buildings and also for the development of new programs and schools at these institutions. His interest in the University of Georgia was sparked by meeting Andrew Patterson, a physics professor from the university, while Peabody was attending a Southern Education Conference. Peabody accepted an invitation from Patterson to attend the school's centennial celebration in 1885, and at the end of his time in Athens, he was committed to helping the institution achieve greater stature. By the 1900s Peabody's philanthropic work in education included serving as the treasurer for three boards: the Southern Education Board, the General Education Board, and the Negro Rural School Fund. In 1903 he was granted honorary degrees by both Harvard University in Cambridge, Massachusetts, and Washington and Lee University in Lexington, Virginia.
Peabody Award
interest in the education system of his native state led Peabody to become one of the University of Georgia's main benefactors. The Peabody Awards, the most prestigious awards given in broadcasting, are awarded by the Grady College of Journalism and Mass Communication at the University of Georgia and bear not only Peabody's name but also his likeness on the medals. The awards were first given out in 1941. His adopted daughter, Marjorie Peabody Waite, served on the first Peabody advisory board and commissioned the design of the medals. Peabody was also awarded an honorary degree from the University of Georgia and made a life trustee of the university by a special legislative act in 1906.
In 1921 Peabody married Katrina Trask, the widow of Spencer Trask, at Yaddo, an artists' community founded by the Trasks on their 400-acre estate in Saratoga Springs, New York. Katrina Trask, who had been in frail health, died on January 8, 1922, less than a year after their marriage.
In 1923 Peabody purchased a residence at Warm Springs, where he died on March 4, 1938. His ashes were later interred at Yaddo, in a grave near his wife.
George Foster Peabody Awards
More in Radio
WSB Radio
Georgia Radio Hall of Fame
J. B. Fuqua (1918-2006)
WAOK
Media Gallery: George Foster Peabody (1852-1938)
"George Foster Peabody (1852-1938)," Broadcasting and Cable, May 26, 2003.
Louise Ware, George Foster Peabody: Banker, Philanthropist, Publicist (Athens: University of Georgia Press, [1951].)
Devaney, Sheila. "George Foster Peabody (1852-1938)." New Georgia Encyclopedia. 09 August 2013. Web. 14 January 2021.
"Blind Willie" McTell (1898-1959)
Tina McElroy Ansa (b. 1949)
Preservation Laws
Maxine Yalovitz-Blankenship
Paige H. Harvey
Judaism and Jews
The Sacred Harp
Public School Buildings
Lanier Meaders (1917-1998)
Millard Grimes (b. 1930)
Clayton McMichen (1900-1970)

redpajama_set_name: RedPajamaCommonCrawl


Homes for sale in Hallmark Estates, a neighborhood in Rock Hill, SC, are displayed below and updated multiple times a day from the CarolinaMLS.
For more information about any of these Hallmark Estates homes for sale, just click the "Request More Information" button when viewing the details of a property. We can provide you with disclosures, past sales history, dates and prices of homes recently sold nearby in Rock Hill, and more.
And, for your convenience, register for a free account to automatically receive email alerts whenever new Hallmark Estates listings come on the market that match your search criteria.


RECENTLY THE PRIMARY HEALTH CARE CENTRE IN WATERHEN HELD A WELLNESS DAY. THE DAUPHIN CLINIC PHARMACY PHARMACIST TREVOR SHEWFELT ATTENDED THE EVENT TO HELP ANSWER QUESTIONS ANYONE HAD. THE DAUPHIN CLINIC PHARMACY ALSO DONATED ITEMS FOR THE DOOR PRIZES.


text:
La Florida State Road 826 (State Road 826, SR-826 ou FL-826) est une route d'État de Floride. Elle dessert la région de grand Miami, en contournant une grande section de la ville par le nord-ouest. Elle possède une section autoroutière longue de 25 miles, ce qui fait de la 826 la plus longue autoroute du grand Miami hors Interstates, à l'exception du Florida's Turnpike. Une petite section à boulevard urbain se poursuit dans North Miami Beach, ce qui porte sa longueur totale à 48.17 kilomètres (29.93 miles) .La route 826 est une route majeure du réseau de Miami, puisqu'elle effectue une longue boucle au nord-ouest de la ville, en passant dans les banlieues nord et ouest de Miami. Elle relie la région à Kendall, où elle se termine sur la U.S. Route 1, passe dans Hialeah, puis passe dans le Golden Glades Interchange, qui permet l'accès à l'interstate 95 et au Florida's Turnpike.La section autoroutière est mieux connue sous l'appellation de la Palmetto Expressway. La section dans North Miami Beach, quant à elle, est appelée North Miami Beach Boulevard, Northeast 163rd Street et Sunny Isles Causeway .

Tracé

Section autoroutière (Palmetto Expressway)
Le terminus sud de la route 826 est situé à une intersection avec la U.S. Route 1, à la frontière entre Pinecrest et Kendall. Elle se dirige ensuite plein nord en passant sous la route 878 de Floride. Elle croise par la suite la route 874 dans un échangeur partiel, puis continue sa route vers le nord en étant une autoroute à accès limité, passant à l'est de Westchester et à l'ouest de West Miami. 4 miles au nord de sa jonction avec la 874, elle croise la U.S. Route 41 et la route 836 en moins d'un mile d'intervalle. Pour le prochain mile vers le nord, elle suit le secteur ouest de l'Aéroport international de Miami, puis passe à l'ouest de Miami Springs. Toujours en se dirigeant vers le nord, elle devient le principal axe nord-sud de Hialeah, banlieue majeure de Miami. Elle croise ensuite l'interstate 75 et la route 924, à Miami Lakes. Ce point est d'ailleurs le terminus sud de l'I-75, qui se poursuit jusqu'à la frontière canadienne.1 mile au nord de l'échangeur 826/924/I-75, elle tourne abruptement vers l'est dans un tournant à 90°, et c'est le premier tournant de la 826 depuis son terminus sud. En se dirigeant maintenant vers l'est, elle passe au nord de l'aéroport d'Opa-locka, puis possède quelques échangeurs dans Miami Gardens. C'est dans cette ville que la section autoroutière se termine, alors qu'elle passe dans le Golden Glades Interchange, qui permet l'accès à l'interstate 95, la principale autoroute nord/sud du grand Miami, et aussi au Florida's Turnpike vers le nord. Ce point est d'ailleurs le terminus sud du Turnpike et la fin de l'autoroute en direction est pour la 826 .

Extension dans North Miami Beach
Une fois passé l'échangeur, elle devient un boulevard urbain dans Biscayne Gardens et North Miami Beach. Elle devient la NE 167th Street, orientation ouest-est qu'elle garde pour 1 mile et demi, puis bifurque légèrement vers le sud-est pour atteindre la hauteur de la NE 163th Street, orientation qu'elle gardera pour un mile environ. Elle croise par la suite la U.S. Route 1, le Biscayne Boulevard, soit une artère majeure des villes côtières du grand Miami. Elle devient par la suite une route à 8 voies surélevée nommée la Sunny Isles Causeway, reliant à la ville du même nom (Sunny Isles Beach). La 826 se termine officiellement à sa jonction avec la route A1A tout près de la côte Atlantique .

Historique
La 826 était initialement une simple route reliant Hialeah à Miami Gardens en passant de Opa-locka dans les années 1940.

Disposition des voies
Entre son terminus sud et sa jonction avec la 874, elle possède 6 voies (3-3). Suite à l'échangeur avec la 874, elle s'élargit subitement à une autoroute à plus de 14 voies par moments (7-7), en possédant un réseau de voies de service. Jusqu'à sa jonction avec la 836, elle maintient tout de même 10 voies (5-5), puis tombe à 8 voies suite à l'échangeur pour un court moment. Entre ce point et son échangeur avec l'I-75, elle possède majoritairement 10 voies, mais certains segments de l'autoroute excédent les 12 voies (2-2). Toutefois, de sa jonction avec la I-75 jusqu'au Biscayne Boulevard à North Miami Beach, elle possède 6 voies (3-3). La Sunny Isles Causeway, quant à elle, possède 8 voies (4-4) .

Liste des sorties

Notes et références

Annexes

Bibliographie

Route en Floride
Miami


Today's Firefox for iPhone and iPad users offers enhancements that will make it easier to get you to what you want faster, from new links within your library and managing your logins and passwords, plus deleting your history as recent as the last hour.
With today's release, we made it easier to clear your web history with one tap on the history page. In the menu or on the Firefox Home page, tap 'Your Library', then 'History', and 'Clear Recent History'.
Because we all make wrong turns on the web from time to time, you can now choose to delete your history from only the last hour, that specific day, and the one before or, as it has always been, your full browsing history.
Everyone likes a shortcut that gets you quickly to the place you need to go. We created links in your library to get you to your bookmarks, history, reading list and downloads all from the Firefox Home screen.
We simplified the place where you can find your logins and passwords in the menu. Go to the menu and tap 'Logins & Passwords'. Also, from there you can enable Face ID or password authentication in Settings to keep your passwords even more secure. It's located in the Face ID & Passcode option.
To get the latest version of Firefox for iOS, visit the App Store.


Dye eggs a light color; let dry.
Wrap and tie string around each egg and dye again in a darker shade.
Remove string after both the eggs and the string are completely dry.
Apply a light dab of glue to leaf and adhere to egg surface.
Wrap egg tightly with pantyhose and rubber-band or knot on the back to keep taut.
Submerge egg in dye until depth of color is achieved.
Remove egg from dye, carefully pull off stocking, and discard the leaf right away; let dry.
Squeeze fabric glue onto egg in thick stripes or desired design, then place in a darker shade.
Once depth of color is achieved, remove egg from dye. Let dry, then carefully peel the glue off the egg.


I have attached list of possible stations, prepared by my Registrar (Mr Khan). Please make sure you can talk up to 5 mints about each topic, some of stations are unexpected like Jehovah's Witnesses: Child with B thalassemia,sickle cell crisis - tonsillectomy issues( I had it as a very first station under pediatric, it took few mins for me to be back on the track!
3. Diagnosis and Management of Thyroid nodule.


text:
Maria de Lourdes Martins Cruz, Mana Lou () genannt, (* 1962 in Açumanu, Portugiesisch-Timor) ist eine osttimoresische, römisch-katholische Nonne.

Werdegang
Nach den Wirren nach dem Abzug der Portugiesen aus ihrer Kolonie und dem Einmarsch der Indonesier 1975 fand Maria als Novizin Aufnahme bei den Canossianerinnen. 1985 ging sie in zum Theologiestudium in das Institut der Jesuiten im indonesischen Yogyakarta auf der Insel Java. 1989 kehrte sie in das besetzte Osttimor zurück und gründete mit den Brüdern und Schwestern in Christus ihren eigenen Orden. Nach eigenen Aussagen will Mana Lou mit ihrer Arbeit "die Notlage der Armen durch der Arbeit an den Wurzeln des Problems verbessern". In Dare baute sie mit dem Institute Main Alin lha Kristo (ISMAIK) eine Ausbildungseinrichtung für Mädchen und Jungen auf. Vom ISMAIK werden drei Waisenhäuser in Dare, Aileu and Viqueque betrieben. Die Kinder werden  in Tetum, Katechismus, Landwirtschaft, Kochen und Handarbeiten, wie Nähen und Sticken unterrichtet.

Nach Abzug der Indonesier 1999 gründete Mana Lou im September mit Hilfe des amerikanischen Arztes Daniel Murphy die Bairo-Pite-Klinik für Bedürftige. Täglich werden hier etwa 300 Menschen medizinisch versorgt. Es verfügt auch über eine Apotheke, ein Labor und einen Kreißsaal. Im Mai 2018 musste die Klinik zeitweise schließen, nachdem australische Spender und die Regierung ihre Unterstützung einstellten.

Auszeichnungen
1997 wurde Mana Lou mit dem Friedenspreis von Pax Christi für ihre Arbeit ausgezeichnet. Im Dezember 2009 erhielt sie von Staatspräsident José Ramos-Horta den Sérgio Vieira de Mello Human Rights Award. Am 2. Juli 2018 wurde Mana Lou mit dem Ramon-Magsaysay-Preis geehrt.

Einzelnachweise

Römisch-katholischer Geistlicher (20. Jahrhundert)
Römisch-katholischer Geistlicher (21. Jahrhundert)
Person des Christentums (Osttimor)
Römisch-katholische Kirche in Osttimor
Osttimorese
Geboren 1962
Frau


99Strategy.biz added a new latest industry research report that focuses on "Profile Projectors market " and provides in-depth Global Profile Projectors market analysis and future prospects of Profile Projectors market 2017. The research study covers significant data which makes the document a handy resource for managers, analysts, industry experts and other key people get ready-to-access and self-analyzed study along with graphs and tables to help understand market trends, drivers and market challenges. The research study is segmented by Application/ end users Machinery Manufacturing, Instrumentation, Watch Industry, Others, products type Vertical, Digital, Horizontal, Tabletop, Others and geographies like United States, China, Europe, Japan, Korea & Taiwan.
The research covers the current market size of the Global Profile Projectors market and its growth rates based on 5 year history data along with company profile of key players/manufacturers such as AOI Systems Limited (UK), Ayonis (France), baty Bowers Group (UK), Carl Zeiss Industrielle Messtechnik GmbH (Germany), DELTRONIC (USA), Dr. Heinrich Schneider Messtechnik GmbH (Germany), HAIDA EQUIPMENT CO., LTD (China), INNOVATEST Europe BV (Netherlands), Leader Precision Instrument Co. Ltd (China), Mitutoyo (Japan), Nikon Metrology (Japan), Optical Gaging Products (USA), SmartVision S.r.l. (Italy), STARRETT (USA), Tesa (Switzerland). The in-depth information by segments of Profile Projectors market helps monitor future profitability & to make critical decisions for growth. The information on trends and developments, focuses on markets and materials, capacities, technologies, CAPEX cycle and the changing structure of the Global Profile Projectors Market.
The study provides company profiling, product picture and specifications, sales, market share and contact information of key manufacturers of Global Profile Projectors Market, some of them listed here are AOI Systems Limited (UK), Ayonis (France), baty Bowers Group (UK), Carl Zeiss Industrielle Messtechnik GmbH (Germany), DELTRONIC (USA), Dr. Heinrich Schneider Messtechnik GmbH (Germany), HAIDA EQUIPMENT CO., LTD (China), INNOVATEST Europe BV (Netherlands), Leader Precision Instrument Co. Ltd (China), Mitutoyo (Japan), Nikon Metrology (Japan), Optical Gaging Products (USA), SmartVision S.r.l. (Italy), STARRETT (USA), Tesa (Switzerland). The market is growing at a very rapid pace and with rise in technological innovation, competition and M&A activities in the industry many local and regional vendors are offering specific application products for varied end-users. The new manufacturer entrants in the market are finding it hard to compete with the international vendors based on quality, reliability, and innovations in technology.
Global Profile Projectors (Thousands Units) and Revenue (Million USD) Market Split by Product Type such as Vertical, Digital, Horizontal, Tabletop, Others. Further the research study is segmented by Application & Other with historical and projected market share and compounded annual growth rate.
Geographically, this report is segmented into several key Regions, with production, consumption, revenue (million USD), and market share and growth rate of Profile Projectors in these regions, from 2012 to 2022 (forecast), covering United States, China, Europe, Japan, Korea & Taiwan and its Share (%) and CAGR for the forecasted period 2017 to 2022.
Chapter 13, 14 and 15, Profile Projectors sales channel, distributors, traders, dealers, Research Findings and Conclusion, appendix and data source.


text:
package metrics

import (
	log "github.com/Sirupsen/logrus"
	"github.com/rcrowley/go-metrics"

	"time"
)

// CounterByMode - container for mode counters, registry and flush interval
type CounterByMode struct {
	Counters      map[string]metrics.Counter
	registry      metrics.Registry
	flushInterval time.Duration
}

// NewModeCounter - returns new counter instance
func NewModeCounter(modes []string) *CounterByMode {

	registry := metrics.NewRegistry()
	counters := make(map[string]metrics.Counter)

	for _, v := range modes {
		counter := metrics.NewCounter()
		counters[v] = counter
		registry.GetOrRegister(v, counter)
	}

	c := &CounterByMode{
		Counters:      counters,
		registry:      registry,
		flushInterval: 5 * time.Second,
	}

	log.Debug("new counter created, registration successful")

	return c
}

// Count - counts requests based on mode
func (c *CounterByMode) Count(mode string) {
	c.Counters[mode].Inc(1)
}

// Init initializes logging
func (c *CounterByMode) Init() {
	go func() {
		for _ = range time.Tick(c.flushInterval) {
			m := c.Flush()
			log.WithFields(log.Fields{"counters": m.Counters}).Info("hoverfly metrics")
		}
	}()
}

// Stats - holds information about various system metrics like requests counts
type Stats struct {
	Counters    map[string]int64   `json:"counters"`
	Gauges      map[string]int64   `json:"gauges,omitempty"`
	GaugesFloat map[string]float64 `json:"gaugesFloat,omitempty"`
}

// Flush gets current metrics from stats registry
func (c *CounterByMode) Flush() (h Stats) {

	counters := make(map[string]int64)
	gauges := make(map[string]int64)
	gaugesFloat := make(map[string]float64)

	c.registry.Each(func(name string, i interface{}) {
		switch metric := i.(type) {
		case metrics.Counter:
			counters[name] = metric.Count()
		case metrics.Gauge:
			gauges[name] = metric.Value()
		case metrics.GaugeFloat64:
			gaugesFloat[name] = metric.Value()
		}
	})

	h.Counters = counters
	h.Gauges = gauges
	h.GaugesFloat = gaugesFloat
	return
}

redpajama_set_name: RedPajamaGithub


text:
Mikhail Khovanov (; born 1972) is a Russian-American professor of mathematics at Columbia University who works on representation theory, knot theory, and algebraic topology. He is known for introducing Khovanov homology for links, which was one of the first examples of categorification.

Education and career
Khovanov graduated from Moscow State School 57 mathematical class in 1988. He earned a PhD in mathematics from Yale University in 1997, where he studied under Igor Frenkel.

Khovanov was a faculty member at UC Davis before moving to Columbia University.

He is a half-brother of Tanya Khovanova.

References

External links
Khovanov's faculty page at Columbia.
List of Khovanov's publications.

1972 births
Living people
20th-century American mathematicians
21st-century American mathematicians
Topologists
Columbia University faculty
Yale University alumni


all that was there was a Post Office, a cheap Hotel, and an ice cream stand.
No traffic lights, no gas stations, no stores. The town right next door, is Cato.
a hardware store, a pizza place, a Diner and a movie rental place.
On this trip back, some of the nostalgia was still there, and some things were a little disappointing.
I decided to go into Cato first and work my way toward Meridian.
The first photo I took was of the four corners of Town.
From this intersection, you can see just about all of Cato. NY Pizzeria on the left with THE BEST pizza around. The full service gas station across the street! Yes, that's right, in all these years that is one of the things that hasn't changed! They actually still come out and pump your gas for you!
Can you imagine how great that would be for us Moms in the dead of winter with babies in carseats?!
Gotta love small town livin'.
but the Hardware store was still there.
Another change was the water tower. They took down the big old fashioned silver one with the name CATO emblazoned in bold black letters and replaced it with a modern looking blue one that you can barely read.
has remained the same, I have always loved the architecture.
So far it had been a pleasant trip, but I knew what came next.
I knew I was going back to a place I had long ago put behind me.
As I entered the Village of Meridian, it was a little surreal.
Buildings like this one and the Post Office were exactly the same as they had always been.
I knew who lived in just about every single house on at least 5 streets next to mine.
That was one thing I actually loved and miss about my childhood.
It was great growing up in the country.
and play kick ball in the summer with room for all the bases.
Those are the things that I miss.
I can't help but think that maybe I didn't really know any of my neighbors at all.
When I pulled up, I immediately saw what the years of neglect and abuse had done to the outside of this place where I had spent the first 20 years of my life.
finally seemed to match the way it had always felt on the inside.
The memories I have from my youth taught me a lot.
Like how you never really know anyone or what they're capable of, unless you live with them.
and said it was a pack of lies.
They would never believe that he could be responsible for those things."
And that statement is so true. In my case, everyone loved my Mother.
She was funny and outgoing and very smart with words.
She was an artist, she could paint a picture of how she wanted others to see her...and they did.
believe her capable of the things that were our day to day reality.
And that's okay, I'm long past the point of needing validation. I know my truth.
However, child abuse and domestic violence are still not talked about enough.
There is a shame and a silence that goes along with them and I don't understand it.
Why can't I speak about my life? Why should I have to hide what happened?
When I realized the answers to those questions were "you can" and "I don't", I truly began to heal.
I am okay talking about where I came from and what happened to me.
My child has never known fear, never cried herself to sleep.
that she is loved beyond measure.
where I spent so many of my childhood hours.
I was happy to see that a lot of the original pieces were still there, like the merry-go-round and the teeter totters (seesaws).
This lovely little tree was still there too.
It was a metaphor for my life back then.
and thinking that it must feel as lonely and out of place as I do.
I don't feel that way anymore.
but that house in the background of this photo never was and never will be my home.
No, my journey was my search for the end of the cycle and a beginning to love.
and I have finally made my way home.
"My long journey home has finally ended with you.
I look beyond to see my past is barely in view."
My name is Paige Everson. I am a happy Wife, a proud Mommy, a lover of lighthouses, fleamarkets, poetry and peanut butter with chocolate! I hate holes in my socks and when my seatbelt gets twisted inside that plastic clippy thing. I have always loved being creative. I think art can manifest itself in a multitude of forms. I can't remember a time in my life when I did not write. Whether it be poems or short stories, writing saved me in so many ways. I know it will always be a huge part of my life. I also took dance for a little over ten years including ballet, tap, jazz and modern. I have the fondest memories of Saturday morning dance class and end-of-year recitals, where I got to dress up and wear make-up! (A HUGE deal to a 6 year old girl!) ;) I love to be creative in my everyday life as well. I am a garage sale/flea market junky. One of my favorite things to do is to take something old and discarded off the side of the road and repurpose it into something new and functional.
Steven Spielberg once said "I don't dream at night. I dream all day. I dream for a living." I think that is how a person feels when work no longer feels like work. When you get to be inspired and creative, make other people happy and still be home with your sweet girl everyday. Well that's just the best you could ever hope for. True to my artistic nature, I have always loved photographs and their nostalgic, story-telling qualities. I just never dreamed I would become a photographer one day. The truth is, I didn't even own a camera until I was in my 30's and pregnant with my daughter. I asked my husband for a camera to document her new life. I could have no way of knowing then, that that one decision and that tiny camera would change my whole life forever!


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Celsius have a quality management system where senior management build, maintain and update the framework to guide the company and its employees towards an improved performance. The principles for the quality management system are derived from the collective experience of senior management and suggested updates from all employees while implementing the quality management whether in the office or on site.
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text:
This Is the Story of a Happy Marriage
Synopses & Reviews
List Price:$16.99
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Publisher Comments
The New York Times bestselling author of State of Wonder, Run, and Bel Canto creates a resonant portrait of a life in this collection of writings on love, friendship, work, and art.
"The tricky thing about being a writer, or about being any kind of artist, is that in addition to making art you also have to make a living."
So begins This Is the Story of a Happy Marriage, an examination of the things Ann Patchett is fully committed to — the art and craft of writing, the depths of friendship, an elderly dog, and one spectacular nun. Writing nonfiction, which started off as a means of keeping her insufficiently lucrative fiction afloat, evolved over time to be its own kind of art, the art of telling the truth as opposed to the art of making things up. Bringing her narrative gifts to bear on her own life, Patchett uses insight and compassion to turn very personal experiences into stories that will resonate with every reader.
These essays twine to create both a portrait of life and a philosophy of life. Obstacles that at first appear insurmountable — scaling a six-foot wall in order to join the Los Angeles Police Department, opening an independent bookstore, and sitting down to write a novel — are eventually mastered with quiet tenacity and sheer force of will. The actual happy marriage, which was the one thing she felt she wasn't capable of, ultimately proves to be a metaphor as well as a fact: Patchett has devoted her life to the people and ideals she loves the most. An irresistible blend of literature and memoir, This Is the Story of a Happy Marriage is a unique examination of the heart, mind, and soul of one of our most revered and gifted writers.
"I had been so engaged by Ann Patchett's multifaceted story, so lured in by her confiding voice, that I forgot I was on the job....As the best personal essays often do, Patchett's is a two-way mirror, reflecting both the author and her readers." New York Times Book Review
"Patchett's mastery of nonfiction [is] every bit the equal of her skill as a novelist." Shelf Awareness
"All the essays were a joy to read....No matter your interest, you'll find words in this book that speak to you." Real Simple
"Each of the essays is its own delight and resonates with warmth and humor.…If read straight through, the book presents a lovely and lyrical look at a life well lived." Library Journal
"Readable and candid, Patchett's collection is a joyful celebration of life, love and the written word." Kirkus Reviews
"Reading Patchett is like spending time with a deeply perceptive longtime pal, or a new friend that one instantly connects with." USA Today
"[A] sparkling collection." The New Yorker
"Happy marriage, compelling writing and all worthy endeavor requires hard work. That's Patchett's strength. And she does a fine job." Miami Herald
"Patchett…is one of our best contemporary novelists. This Is the Story of a Happy Marriage reminds us that she is an exceptional writer of nonfiction, too. Her prose is a pleasure to read, regardless of genre." Dallas Morning News
"Novelist Ann Patchett's excellent essay collection ranges from dogs to writing to white-knuckled air travel." Christian Science Monitor
"In this heartfelt collection of autobiographical essays, the novelist opens up about love, friendship, and family, exhibiting the compassionate voice that is a hallmark of her fiction." O, the Oprah Magazine
"It is a feat that Ann Patchett remains so lovable as a narrator, and so engaging as a storyteller, when writing about her excellent career, personal life, dog, and husband." Newsday
"Patchett's is a no-nonsense voice: clear, sane, companionable.…[T]he funny, frank and nervy 'The Getaway Car' (possibly worth the book's price) plunges readers, roller-coaster style, into the story of Patchett's writing life — essentially, this collections real subject." San Francisco Chronicle
"[I]n this terrific, wide-ranging collection, Patchett demonstrates how a pro does it." NPR's Fresh Air
"All of the essays, which have been collected from her magazine work over two decades, are excellent. Patchett writes enviable prose — fluid, simple, direct, clear, and fearless…" Esquire.com
"Ann Patchett most definitely has something to say, in her fully realized and beautiful voice." Huffington Post
"Writing of loss and of the complications of love, Patchett lets down her guard…and opens both her sense of humor and her heart." Columbus Dispatch
"Wit-filled and elegantly executed" Entertainment Weekly
"The best advertisement for Ann Patchett's new collection of nonfiction is anything else Ms. Patchett has written....Ms. Patchett's style is not overly confessional, but it is beguiling in ways that make her sound like someone you'd want to know." New York Times
Blending literature and memoir, Ann Patchett, author ofState of Wonder, Run, andBel Canto, examines her deepest commitments to writing, family, friends, dogs, books, and her husband creating a resonant portrait of a life inThis is the Story of a Happy Marriage.
This Is the Story of a Happy Marriage takes us into the very real world of Ann Patchett s life. Stretching from her childhood to the present day, from a disastrous early marriage to a later happy one, it covers a multitude of topics, including relationships with family and friends, and charts the hard work and joy of writing, and the unexpected thrill of opening a bookstore.
As she shares stories of the people, places, ideals, and art to which she has remained indelibly committed, Ann Patchett brings into focus the large experiences and small moments that have shaped her as a daughter, wife, and writer.
Reese Witherspoon Book Club Pick
Blending literature and memoir, Ann Patchett, author of State of Wonder, Run, and Bel Canto, examines her deepest commitments--to writing, family, friends, dogs, books, and her husband--creating a resonant portrait of a life in This is the Story of a Happy Marriage.
This Is the Story of a Happy Marriage takes us into the very real world of Ann Patchett's life. Stretching from her childhood to the present day, from a disastrous early marriage to a later happy one, it covers a multitude of topics, including relationships with family and friends, and charts the hard work and joy of writing, and the unexpected thrill of opening a bookstore.
Blending literature and memoir, New York Times bestselling author Ann Patchett, author of State of Wonder, Run, and Bel Canto, examines her deepest commitments--to writing, family, friends, dogs, books, and her husband--creating a resonant portrait of a life in This is the Story of a Happy Marriage.
Stretching from her childhood to the present day, from a disastrous early marriage to a later happy one, This is the Story of a Happy Marriage covers a multitude of topics, including relationships with family and friends, and charts the hard work and joy of writing, and the unexpected thrill of opening a bookstore.
"I had been so engaged by Ann Patchett's multifaceted story, so lured in by her confiding voice, that I forgot I was on the job. ...] As the best personal essays often do, Patchett's is a two-way mirror, reflecting both the author and her readers." -- New York Times Book Review
Blending literature and memoir, Ann Patchett, author of State of Wonder, Run, and Bel Canto, examines her deepest commitments — to writing, family, friends, dogs, books, and her husband — creating a resonant portrait of a life in This is the Story of a Happy Marriage.
Ann Patchett is the author of six novels and three works of nonfiction. She is the winner of the PEN/Faulkner Award, England's Orange Prize, and the Book Sense Book of the Year, and was named one of Time magazine's 100 Most Influential People in the World. Her work has been translated into more than thirty languages. She is the co-owner of Parnassus Books in Nashville, Tennessee, where she lives with her husband, Karl, and their dog, Sparky.
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Average customer rating 5 (1 comments)
kevinrbrown , March 08, 2015 (view all comments by kevinrbrown)
Patchett's collection is solid throughout, something that can't be said about most essay collections. Her essay on writing, "The Getaway Car," is outstanding and should be required reading for everyone who even thinks about writing. If you're interested in education, bookstores, reading, dogs, becoming a police officer, writing, or how Patchett found a happy marriage, this is the book for you.
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text:
Republican Candidates Opening Up About Family Struggles With Addiction
A viral video of New Jersey Gov. Chris Christie (R) railing against how society treats drug addiction has generated newfound interest in how presidential candidates have dealt with the issue.
In Christie's case, he described a very successful law-school friend who became addicted to pain-killers and having to go to his funeral.
He compared his friend's drug addiction to his mother getting lung cancer after being addicted to cigarettes.
"We know the lung cancer was caused by the smoking," Christie said in a video posted by The Huffington Post last Friday that has since accumulated almost 6 million views.
"But no one came to me and said, 'Hey, listen, your mother was dumb," he said. "Somehow, if it's heroin or cocaine or alcohol, we say, 'They decided it. They're getting what they deserved.'"
Former Florida Gov. Jeb Bush (R) since gave an emotional interview to The Huffington Post about his daughter Noelle's struggle with drug addiction.
"I don't know what it's like to lose a daughter, but I almost did," Bush said on board his campaign bus.
"My daughter … she went through hell. And so did her mom and so did her dad," he said. "It became very public when I was governor. And it wasn't easy. I visited her in jail. I never expected to see my beautiful daughter in jail."
Bush added: "I have so many friends and so many people I've known that have gone through this. It crosses all barriers, all lines, all races, all income. So, it's not easy. With my daughter, she's doing fine now. But it's with you for the rest of your life. "
Jeb Bush On Addiction
Jeb Bush on addiction: "I don't know what it's like to lose a daughter, but I almost did."
Posted by HuffPost on Thursday, November 5, 2015
And in a CNN interview on Thursday, Sen. Ted Cruz (R-Texas) discussed struggling with his half-sister Miriam's addiction and her eventual death.
Cruz, who has opened up about the subject before, said, "It's a horrible disease, and I've seen it first-hand."
"Her parents got divorced when she was a little girl, and Miriam was always very angry about it. And it consumed her. And she smart. She was beautiful. And yet her whole life she lived basically as an angry teenager. She was sort of frozen, emotionally, in a state of rebellion," Cruz said.
"She made decision after decision that was the wrong decision. And she struggled her whole life with drug and alcohol addiction. She was in and out of prison for petty crimes," he continued. "But she kept associating with people who were really bad actors."
Cruz said that when he was a young adult, his half-sister was actually living in a crack house in Philadelphia. Cruz said he and his dad visited her there to try and urge her to turn her life around.
"She, a few years ago, overdosed one night. And [her son] Joey came to the apartment and found her dead," Cruz said.