text:
\section{Introduction}
Attempts to recover statistical mechanics from the underlying unitary dynamics of a quantum system are around since the inception of quantum theory with the pioneering approaches of both von Neumann~\cite{Vonneumann:1929} and Schr\"{o}dinger~\cite{Schrodinger:1927}.
Although these works showed impressive foresight, until relatively recently these foundational studies were almost forgotten and seen as irrelevant due to the fact that unitary evolution was not relevant over dynamical time scales in the laboratory.
Arguments for the validity of statistical mechanics predominantly consisted of invoking coupling to the larger bath of the universe and hence thermalisation by dissipation.

In the past two decades, these foundational questions have seen an unprecedented resurgence in interest by theorists from several different scientific communities, ranging from condensed matter physics to quantum information \cite{Zelevinsky1996,Polkovnikov:2011,Yukalov:2011,Eisert:2015,Goold:2016,Gogolin:2016,Borgonovi:2016,Alessio:2016}.
This revival is due, in no small part, to great advances in experimental ultra-cold atomic physics \cite{Lewenstein:2007} where pioneering experiments were successful in generating and probing coherent unitary dynamics over long timescales \cite{Greiner:2002,Kinoshita:2006,Trotzky:2012,Kaufman2016}.
This includes an experimental realization \cite{Kinoshita:2006} of the Lieb-Liniger model of interacting bosons in one dimension, in which the existence of an extensive set of conserved quantities, due to the integrability of the model, renderes the dynamics non-ergodic \cite{Rigol:2008}.

Experimental motivations aside, there has also been developments in theoretical condensed matter physics which have forced us to carefully think about the foundations of statistical mechanics beyond the paradigm of integrable systems.
In particular Basko, Aleiner and Altshuler have demonstrated that Anderson localisation \cite{Anderson:1958} is stable in the presence of interactions \cite{Basko:2006} leading to a new type of transition to a phase which is known as many-body localization (MBL) \cite{Nandkishore:2015,Vosk:2015,Altman:2015}.
Interestingly this transition is between an ergodic and a non-ergodic phase \cite{Oganesyan:2007} and has led to an intense interest in the phenomenology of ergodicity and its breaking in quantum dynamics.

Physically motivated, an approach known as Eigenstate Thermalisation Hypothesis (ETH) has proven to be popular amongst researchers from this community.
The ETH was born out of a realization by Berry \cite{Berry:1977}, who postulated that, in the semi-classical limit of quantum systems with chaotic classical counterparts, the Wigner function evaluated on eigenstates reduces to the micro-canonical distribution.
This was extended to arbitrary systems by Deutsch \cite{Deutsch:1991}, who proposed to assume that generic eigenstates of ergodic systems are like eigenstates of full random matrices.
Building on these ideas Srednicki formulated what is now known as the ETH, which is an ansatz on the behavior of matrix elements of observables with the consequence that ergodic systems can show thermal behavior at the level of individual eigenstates \cite{Srednicki:1994,Srednicki:1996,Srednicki:1999}.

Another approach, popular in the quantum information and mathematical physics communities, is the concept of normal and canonical typicality \cite{Tasaki:1998,Gemmer:2003, Popescu:2006,Goldstein:2006,Reimann:2008}.
This approach has the advantage of not just replacing one hypothesis (that systems tend to equilibrate to Gibbs states) with another equally unproven one (that systems generically fulfill the ETH), but it replaces the equal a priori probability postulate (all states in a microcanonical shell are equally probable) with a strictly weaker assumption, by showing rigorously, that the overwhelming majority of states in a microcanonical shell have nearly the same properties with respect to certain observables, like, for example, local ones.
However, the generality of the results obtained based on these concepts makes it difficult to apply this approach to concrete systems, as in realistic situations interesting dynamics is usually starting from a highly untypical initial condition.

In addition to the above, in recent years dynamical equilibration of expectation values and density matrices of subsystems under unitary dynamics has been studied extensively \cite{Reimann:2008,Linden:2009,Reimann10,Reimann12,Malabarba2014,Reimann2016} (see also \cite{Gogolin:2016} for a review).
Such equilibration can be rigorously shown to happen if the spectrum of the Hamiltonian fulfills certain non-resonance conditions, and the initial state has overlap with many energy eigenstates or the second most populated eigenstates is occupied with only a small probability (a weaker requirement).
In these results, the equilibrium expectation values or reduced states are given by the diagonal ensemble (also known as infinite time averaged state, dephased state, or pinched state).
How and to which state equilibration occurs, of course is closely connected to whether a system is ergodic or not, which motivates us to consider in more detail the correlations in this diagonal ensemble to study ergodicity breaking.

Concepts of quantum information have been useful in the typicality approach (system-bath entanglement) \cite{Popescu:2006}, the dynamical equilibration approach, and in the ETH approach, for example in studying the volume law scaling of entanglement in eigenstates, the crossover to an area law is a signature of the MBL transition \cite{Luitz:2015}. In a recent work, some of the current authors have proposed a different information theory inspired approach~\cite{Goold:2015}.
The idea is to look at the correlations within the diagonal ensemble to understand non-ergodic behavior in the context of the MBL transition \cite{Goold:2015}. The purpose of the current work is to demonstrate that this concept is more generally useful and can detect ergodicity breaking in a range of scenarios beyond and including MBL.
The formalism offers a fresh approach to ergodicity and its breaking in quantum systems, while at the same time giving us novel insights into the structure of correlations in the equilibrium state of dynamical systems.

\section{Ergodicity and total correlations}
Due to the absence of a universally valid phase space picture in quantum systems it is not obvious how to generalize the concept of ergodicity to the quantum realm, especially in systems that do not have a well defined classical limit.
As was outlined in Ref.~\cite{Goold:2015}, the total correlations in the diagonal ensemble offer a physically meaningful way to define and probe ergodicity and its breaking in quantum systems.
Here we generalize this approach.

\subsection{A condition for ergodicity.}
The (quasi) ergodic hypothesis in classical systems states that over time a system's dynamics uniformly covers its entire phase space so that the (infinite time) time average and the micro-canonical averages agree~\cite{Gallavotti:2013}.
It is thus natural to define ergodicity in quantum systems in an analogous way via the portion of the explored Hilbert space.
A complication is that quantum systems explore all of the available phase space uniformly such that time and microcanonical average agree exactly only for very special initial states.
This naturally leads us to build a notion of ergodicity in quantum systems based on the fraction of the available Hilbert space that is explored, as opposed to classical notion of ergodicity that requires that all of the available phase space is explored uniformly.
The available Hilbert space hereby can be usually naturally defined as, for example, the fixed magnetization or fixed filling fraction subspace if the system has such symmetries.
To define ergodicity via the fraction of Hilbert space that is explored one obviously first needs to devise a way of quantifying the explored fraction.
It is this question that we elucidate in this work, going beyond the initial proposal in Ref.~\cite{Goold:2015}.

For a fixed initial state $\rho$ and non-degenerate Hamiltonian $H$ the diagonal ensemble is defined as
\begin{equation} \label{eq:timeav}
  \omega \coloneqq  \sum_n \ket {E_{n}}\bra {E_{n}} \,\rho\, \ket {E_{n}}\bra {E_{n}} = \lim_{\tau\to\infty} \frac{1}{\tau} \int^{\tau}_{0}dt\, \mathrm{e}^{-itH}\, \rho\, \mathrm{e}^{itH} ,
\end{equation}
where $\ket {E_{n}}$ are the eigenvectors of $H$.
The state $\omega$ is the state that maximizes the von Neumann entropy subject to all constants of motion \cite{PhysRevLett.10-6}.
For pure initial states $\rho=|\Psi\rangle\langle\Psi|$, the inverse purity $1/\mbox{tr}(\omega^2)$ of the diagonal ensemble can be seen as a measure for how spread-out the initial state was over the different eigenstates of the Hamiltonian and it often goes under the apt name of \emph{effective dimension} or \emph{participation ratio}.
If the effective dimension is high, expectation values of observables can be rigorously shown \cite{Reimann:2008,Linden:2009,Polkovnikov:2011,Eisert:2015,Gogolin:2016} to equilibrate on average during the time evolution towards their values in the state $\omega$.
The effective dimension however is not the only way of quantifying the spreading of the initial state.
Another measure is the von Neumann entropy of the diagonal ensemble $S(\omega)=-\sum_n p_n\log_2 p_n$ with $p_n=|\langle E_n|\Psi\rangle|^2$ and derived quantities; this was the route taken in Ref.~\cite{Goold:2015}.

Both of these quantities are special cases of a whole family of entropies, the so-called $\alpha$-Renyi entropies, which for $0<\alpha<\infty$ are defined as
\begin{equation}\label{eq:renyidiagentrop}
  S_\alpha(\rho) \coloneqq \frac{1}{1-\alpha} \log_2(\mbox{tr}(\rho^\alpha)) .
\end{equation}
The $2$-entropy $S_2 = \log_2(1/\mbox{tr}(\rho^2))$ is the log of the inverse purity, the $1$-entropy $S_1 = S$ is the von~Neumann entropy, and the two extreme cases are defined as $S_\infty(\rho) \coloneqq \log_2(1/\|\rho\|_\infty)$ and $S_0(\rho) \coloneqq \log_2(\rank(\rho))$.
The Renyi entropies are monotonically non-increasing as a function of $\alpha$.
In other words, for any fixed $\rho$, it holds that $S_\alpha(\rho) \leq S_{\alpha'}(\rho)$ whenever $\alpha' \geq \alpha$.
For $\psi$ a pure state and $\rho$ a normalized quantum state of a system with Hilbert space dimension $d$, it holds that
\begin{equation}
  0 = S_\alpha(\psi) \leq S_\alpha(\rho) \leq S_\alpha(\mathds{1}_{d\times d}/d) = \log_2(d) .
\end{equation}
Except in the case $\alpha = 0$ the inequalities hold with equality only if $\rho$ is either pure or maximally mixed, respectively.

It is the upper bound that interests us here.
Given a Hamiltonian $H$, an initial state $\rho$ explores all of Hilbert space if $S_\alpha(\omega) = \log_2(d)$.
As said above, this however only happens for very special states for which $\omega$ is maximally mixed.
A natural relaxation of this condition is to demand that for some chosen $0\leq\alpha\leq\infty$ there exists a constant $\lambda > 0$, independent of $N$ and $d$, such that $S_\alpha(\omega) \geq \log_2(\lambda\,d)$, i.e., that the state explores a $\lambda$-fraction of the Hilbert space as measured by the $\alpha$-Renyi entropy.

That this is a sensible condition for ergodicity is further illustrated by the following consideration:
For any fixed initial state $\rho$ and Hamiltonians $H$ with eigenbasis randomly drawn from a unitary invariant ensemble on a Hilbert space of dimension $d$ one can show for the $\alpha=1$ entropy \cite[Eq.~(B6)]{Hayden:2004} and the $\alpha=2$ entropy \cite{Linden:2009} that the probability that the state explores less than half of the available Hilbert space is at least almost exponentially suppressed with growing $d$ (as the Renyi entropies are non-increasing as a function of $\alpha$ this then holds for all $0 \leq \alpha \leq 2$).
That is, any fixed initial state is with high probability ergodic according to our condition with respect to Hamiltonians drawn unitarily at random---as one would expect. To be more precise: Generalizing the considerations from \cite{Goold:2015} we hence demand that a system should be considered $\alpha$-ergodic only if the initial states explore at least a constant fraction of the available Hilbert space in the sense that for some $\lambda$ it holds that $S_\alpha(\omega) \geq \log_2(\lambda\,d)$.  In the models that we will consider the Neel states are suitable initial states.

We have so far defined a family of conditions parametrized by $\alpha$ that appear as natural quantum generalizations of the concept of ergodicity, but have not yet said much about the role of $\alpha$.
Remember that the Renyi entropies are monotonically non-increasing as a function of $\alpha$.
Thus, demanding that, for example, $S_2 \geq \log_2(\lambda\,d)$ is a stronger requirement than demanding that the same scaling holds for $S_1$.
As we will see later, the fact that a system fulfills our condition for ergodicitiy for a given $\alpha$ has direct consequences on the scaling of the total correlations with the number of particles.

\subsection{Total Correlations.}
Phase transitions that involve the breaking of ergodicity, like the MBL transition, have in the past been analyzed with various measures of correlations.
A focus thereby was on the mutual information, which was found to saturate to a constant in Anderson localization, grow logarithmically in time in the MBL phase, and linearly in ergodic phases \cite{DeTomasi2016}.
Further, it decays exponentially with the distance between subsystems in the localized phase, but slower than exponential in the ergodic phase. Here we concentrate on a correlation measure called the total correlations and its Renyi generalizations.
Concretely we define the $\alpha$-Renyi total correlations as
\begin{equation}
  T_\alpha(\rho) \coloneqq \sum_{m=1}^N S_\alpha(\rho_{m}) - S_\alpha(\rho),
  \label{eq:totcor1}
\end{equation}
where $\rho_m$ is the marginal (reduced state) of $\rho$ on site $m$.
In the special case $\alpha=1$ the total correlations have the following operational meaning:
Let $\mathcal{P}$ be the set of all product states of an $N$ partite quantum system, i.e., for spin systems, states of the form $\pi=\pi_{1}\otimes\pi_{2}\dots\otimes\pi_{N}$ and the obvious analogues for fermionic and bosonic systems, then \cite{Modi:2010}
\begin{equation}
  T_1(\rho) = \min_{\pi\in\mathcal{P}} S(\rho\|\pi) .
\end{equation}
where $S(\rho\|\sigma) \coloneqq -\mbox{tr}(\rho\,\log_2 \sigma)-S_1(\rho)$ is the relative entropy between the states $\rho$ and $\sigma$ and it can be thought of as a measure of distinguishability of the two states.
More precisely, the relative entropy quantifies how difficult it is to distinguish between many copies of $\rho$ and many copies of $\sigma$ in a hypothesis testing scenario \cite{Audenaert2012}.
It turns out that there is a unique product state that minimizes the relative entropy in the above expression and this is the product of the reduced states $\rho_{m}$ of $\rho$, i.e., $\pi=\otimes^{N}_{m=1} \rho_{m}$ \cite{Modi:2010}.
In the case $\alpha =1$ the total correlations, can hence be thought of as the distinguishability from the closest product state.
No such straightforward operational interpretation exists for $\alpha\neq1$ to the best of our knowledge.

As we will explain in the next sections, insights into integrability breaking can be obtained through the various Renyi total correlations.

\subsection{Scaling of the total correlations.}
In the following we analyze the total correlations, and in particular $T_1$ and $T_2$, of the diagonal ensemble $\omega$ for Neel initial states in various spin chain models.
One characteristic that will be very insightful is the scaling of the total correlations with $N$.

Inspecting Eq.~\eqref{eq:totcor1} one might expect that the total correlations $T(\omega)$ in the diagonal ensemble should generally scale extensively in the system size $N$, i.e, for large $N$, to leading order, it should scale like
\begin{equation} \label{eq:linearscaling}
  T_\alpha(\omega) \propto N ,
\end{equation}
as $T_\alpha(\omega)$ involves the sum $\sum_{m=1}^N S_\alpha(\omega_{m})$ of the $N$ subsystem entropies.

If a family of systems of increasing size satisfies the condition for ergodicity defined above, then the contribution linear in $N$ from the first sum can be precisely canceled by the $-S_\alpha(\omega)$ term; $S_\alpha(\omega)$ is known as the diagonal entropy~\cite{PolkovnikovReview} and is a measure of localization in the energy eigenbasis.
Consider a quantum spin chain of local dimension $2$ in the zero magnetization subspace~\footnote{The diagonal entropy - or Shannon entropy in the energy eigenbasis, measures delocalization/localization in that basis and therefore its scaling can give information about ergodicity. However, the total correlations and its Renyi generalizations give far more information; in particular it not only scales differently in different phases but also shows divergence of the correlations in the critical region - an interesting phenomenon in its own right which cannot be studied just looking at the diagonal entropy alone.}.
The available Hilbert space dimension is $d = \binom{N}{N/2} = N! / \left(\tfrac{N}{2}!\right)^{2} \geq \sqrt{8\,\pi}\, \mathrm{e}^{-2}\, 2^N/\sqrt{N}$ and $S_\alpha(\omega_{m}) \leq \log_2 2 = 1$, so that if the condition for ergodicity $S_\alpha(\omega) \geq \log_2(\lambda\,d)$ holds, one finds at most the logarithmic scaling
\begin{equation} \label{eq:logscaling}
  T_\alpha(\omega) \leq \log_2(N)/2 - \log_2(\lambda\,\sqrt{8\,\pi}\,\mathrm{e}^{-2}) .
\end{equation}
One furthermore retains a logarithmic scaling for ergodic systems for all other constant magnetization/fillings subspaces $\eta\neq 1/2$ in the case $\alpha=1$ \cite{Goold:2015}.

This sub-extensive scaling can also be understood intuitively: The transport present in ergodic systems correlates the different parts of the system to the extent that they appear, for most times during the evolution, so mixed that the time averaged state starts to resemble a product state.

In conclusion we can say that whenever we see a faster than logarithmic scaling in the $\alpha$-Renyi total correlations of the diagonal ensembles $\omega$ of an initial state from the half filling subspace, then the condition for ergodicity for that value of $\alpha$ is violated.
On the contrary, a logarithmic scaling suggests ergodic behavior.

\section{Examples}
Low-dimensional many-body quantum systems, such as spin-1/2 chains are systems commonly used to study ergodicity breaking phenomena.
In what follows we will always consider dynamics starting from the trivial initial Hamiltonian, $H_{0}$ defined as \begin{equation} \label{eq:trivial}
  H_{0} =\sum^{N}_{i=1}J_zs^{i}_{z}s^{i+1}_{z},\end{equation}
where $s^i$ are spin-1/2 operators, and we choose as an initial state the Neel state $|\Psi_{0}\rangle=|\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\dots\rangle$.
Now imagine a quench where we turn on additional terms denoted by an interaction part $H_{int}$ such that dynamics is initiated and governed by the Hamiltonian $H_{F}=H_{0}+H_{int}$.
We shall build the diagonal ensemble defined by Eq.~\eqref{eq:timeav} by exact diagonalization and then investigate the scaling of the total correlations $T(\omega)$ as defined in Eq.~\eqref{eq:totcor1}, both in the case of the Von Neumann total correlations ($\alpha=1$) and of the $2$-Renyi total correlations ($\alpha=2$).
We choose the initial state $|\Psi_{0}\rangle$ as a Neel state for two principal reasons:
First, in the models we shall consider, the Neel state can be shown to sample eigenstates of $H_F$ at the center of the spectrum and in the half filling subspace~\cite{torresherrera2014}.
In this regime we expect the finite size effects to be minimized.
Second, the Neel state (charge density wave in fermion picture), is by now routinely prepared by experimentalists to study ergodicity breaking, for example in the recent studies of MBL systems~\cite{Schreiber:2015,Smith:2016}.

\subsection{Integrability Breaking}
Let us begin with the following model studied by Santos in 2004 \cite{Santos:2004}.
The model is an XXZ spin chain with open boundary conditions which includes a single defect at the centre of the chain of strength $\epsilon$,
\begin{equation} \label{eq:heisenbergchain}
  H_{F} =\sum^{N}_{i=1}\Big[J_xs^{i}_{x}s^{i+1}_{x}+J_{y}s^{i}_{y}s^{i+1}_{y}+J_zs^{i}_{z}s^{i+1}_{z}\Big]+\epsilon s^{N/2}_{z}.
\end{equation}
The integrability of the chain is broken\cite{Santos:2004}, indicated by a crossover from Poissonian to Wigner-Dyson statistics, for defect strengths which are comparable to the interaction energy.
As the strength of the single defect is increased the system becomes integrable again as the chain is cut into two XXZ chains.
Our theory predicts then that we should see a linear-log-linear behavior in the scaling of the total correlations as we increase the defect strength from zero.
This is indeed what results from the numerical computation of $T_1(\omega)$, shown in the main plot of Fig.~\ref{fig1} for three values of $\epsilon$, $\epsilon=0$, $0.5$ and $10$: $T_1$ scales linearly for the values $\epsilon=0$ and $\epsilon=10$ and approximately logarithmically for $\epsilon=0.5$ as a function of system size. The same happens to the $2$-Renyi total correlations $T_2(\omega)$, shown in the main plot of Fig.~\ref{fig1sp}.

The second model that we consider is the clean XXZ model with next-nearest-neighbour interaction,
\begin{multline} \label{eq:nnn}
  H_{\text{NNN}} =\sum^{N}_{i=1}\Big[J_x s^{i}_{x} s^{i+1}_{x}+J_{y} s^{i}_{y} s^{i+1}_{y}+J_z s^{i}_{z} s^{i+1}_{z}+\\ J_x' s^{i}_{x} s^{i+2}_{x}+ J_{y}' s^{i}_{y} s^{i+2}_{y}\Big].
\end{multline}
For $J_x', J_y'\neq0$ integrability is broken and the scaling of the total correlations $T_1(\omega)$ with the system size is logarithmic, as is shown in the inset of Fig.~\ref{fig1}.
Also in this model we see an analogous behaviour for the $2$-Renyi total correlations $T_2(\omega)$, which are logarithmically scaling with the system size (see the inset of Fig.~\ref{fig1sp}).

\begin{figure}[t]
\includegraphics[width=1\columnwidth]{fig1Linear.pdf}
\caption{(Color online) The Von Neumann total correlations of the diagonal ensemble starting with the Neel state for an XXZ chain with defect of strength $\epsilon$ placed at centre of the chain (Eq.
\eqref{eq:heisenbergchain} with parameters $J_x=J_y=1$ and $J_z=0.5$).
When the defect strength is zero or very strong the model is integrable, which is reflected in a linear scaling of the total correlations, and when it is comparable with the interaction energy it shows a logarithmic growth indicative of ergodic dynamics.
\textit{Inset. } Total correlations for an XXZ chain with next-nearest-neighbour interaction (Eq.
\eqref{eq:nnn} with parameters $J_x=J_y=1$, $J_z=0.5$ and $J_x'=J_y'=1$, compared to the same model with $J_x'=J_y'=0$).
The model is non-integrable and thus the scaling of the total correlations is logarithmic in the system size.}
  \label{fig1}
\end{figure}

\begin{figure}
\includegraphics[width=1\columnwidth]{{fig1Linearsp}.pdf}
\caption{(Color online) The $2$-Renyi total correlations of the diagonal ensemble starting with the Neel state for an XXZ chain with defect of strength $\epsilon$ placed at centre of the chain (Eq.
\eqref{eq:heisenbergchain} with parameters $J_x=J_y=1$ and $J_z=0.5$).
When the defect strength is zero or very strong $T_2$ scales linearly with system size and when it is comparable with the interaction energy it scales logarithmically.
\textit{Inset. } Total correlations for an XXZ chain with next-nearest-neighbour interaction (Eq.
\eqref{eq:nnn} with parameters $J_x=J_y=1$, $J_z=0.5$ and $J_x'=J_y'=1$, compared to the same model with $J_x'=J_y'=0$).
The scaling of the total correlations is logarithmic in the system size.}
  \label{fig1sp}
\end{figure}

In both cases of integrability breaking, the total correlations displays the predicted behaviour.

\subsection{Many-body localization}
Let us now consider models which have an MBL transition that separates an ergodic phase and a non-ergodic one where a sufficient number of local integrals of motion exists in order to have a breaking of the ETH~\cite{ros2015integrals}.
We look at a system with the Hamiltonian
\begin{equation} \label{eq:mbl}
  H_{\text{MBL}} =\sum^{N}_{i=1}\Big[J_x s^{i}_{x} s^{i+1}_{x}+J_{y} s^{i}_{y} s^{i+1}_{y}+J_z s^{i}_{z} s^{i+1}_{z}+h_i s^i_z\Big],
\end{equation}
where $h_i\in[-h,h]$ is a disordered field (Heisenberg model with random fields) or $h_i=h\cos{(2\pi \phi^{-1} i+\delta)}$, where $\phi$ is the golden ratio and $\delta$ is a random phase in $[0,2\pi)$, that is a pseudo-disordered cosine field (Aubry-Andr\'e model).
For both models we compute the total correlations for the diagonal ensemble with the Neel initial state, averaging over many disorder or pseudo-disorder realizations, the latter obtained through the random phase $\delta$ ($10^5$ realizations for $N\leq 12$, $10^4$ for $N=14$ and $250$-$1000$ for $N=16$).
The results for the Von Neumann total correlation rescaled with the system size, $T_1(\omega)/N$, are shown in Figs.~\ref{fig2} and \ref{fig3} respectively for the two models, as a function of the disorder or quasi-disorder strength.

We note two features: the curves collapse for $h\geq h^*$, indicating a linear scaling of the total correlations and thus non-ergodicity, and $T_1(\omega)/N$ peaks at a value $h^*(N)$.
Remarkably, the presence of a peak can be understood as a divergence of correlations at the MBL transition point and its asymptotic position in the infinite-size limit gives the transition value $h_c$~\cite{Goold:2015}.
We are able to perform such extrapolation (see Fig.~\ref{fig:peaksp}), thus obtaining $h^\text{H}_c= \lim_{N\to\infty} {h^\text{H}}^*=4.0\pm0.2$ for the random potential and $h^\text{AA}_c= \lim_{N\to\infty} {h^\text{AA}}^* =4.5\pm0.9$ for the Aubry-Andr\'e potential. Note that for the latter case the extrapolation suffers from much larger errors due to the smaller movement of the peak of the finite-size data with respect to its error.

For the Heisenberg model with random fields the transition value has been estimated through other numerical evidence \cite{Luitz:2015,Pal:2010,pietracaprina2016forward} to be equal to $h^\text{H}_c=3.7(2)$ at the center of the band for the parameters that we used, although its actual value could be larger ($h^\text{H}_c\geq 4.5$ according to~\cite{Devakul2015}); an equivalent high-quality numerical result is not available for the Aubry-Andr\'e model, although experimental works find the localization transition at similar values~\cite{Schreiber:2015}.
Interestingly, as soon as interactions are introduced, the Aubry-Andr\'e model acquires almost identical features to the Heisenberg with random fields model first studied by total correlations in \cite{Goold:2015}.
Finally, for both models, for weak \mbox{(quasi-)} disorder ($h\lesssim h^*$), the scaling of the total correlations is logarithmic, implying an ergodic phase.

\begin{figure}[t]
\includegraphics[width=1\columnwidth]{{fig2_am_delta1.}.pdf}
\caption{(Color online) The Von Neumann total correlations of the diagonal ensemble, starting with a Neel state, for the Heisenberg model with random fields (whose Hamiltonian is Eq.
\eqref{eq:mbl} with $h_i\in[-h,h]$ and $J_x=J_y=J_z=1$), rescaled with the system size. The markers on the top axis denote the positions of the local peak $h^*(N)$.
The curves show a system-size-dependent peak (see Fig.~\ref{fig:peaksp}) and collapse for $h\gtrsim2.5$.
\textit{Inset.
} System size scaling of the total correlations for three example values of $h$, showing a logarithmic scaling deep in the delocalized phase and a linear scaling for disorder values near the transition (which is at $h_c\approx3.7$) and in the localized phase.}
  \label{fig2}
\end{figure}

\begin{figure}[t]
\includegraphics[width=1\columnwidth]{{fig3_aam_delta1.}.pdf}
\caption{(Color online) The Von Neumann total correlations of the diagonal ensemble, starting with a Neel state, for the Aubry-Andr\'e model (whose Hamiltonian is Eq.
\eqref{eq:mbl} with the cosine $h_i$ fields and $J_x=J_y=J_z=1$), rescaled with the system size.
The curves show a system-size-dependent peak and collapse for $h\gtrsim3.5$.
\textit{Inset.
} System size scaling of the total correlations for three example values of $h$, showing a logarithmic scaling deep in the delocalized phase and a linear scaling in the localized phase.}
  \label{fig3}
\end{figure}

Let us now consider the $2$-Renyi total correlations, focusing first on the Heisenberg model with random fields. The total correlations rescaled by the system size $T_2(\omega)/N$ are shown in Fig.~\ref{fig2sp}, showing a collapse for $h\gtrsim 2$ for the available system sizes, to be compared with an analogous behaviour of $T_1(\omega)/N$, where the collapse point is $\approx 2.5$.
For a system of infinite size, one would expect that the collapse points (or equivalently the peak positions) should be the same for all total correlations $T_\alpha$; due to the stronger ergodicity requirement of higher-$\alpha$ Renyi entropies, however, it is understandable that $T_2$ gives an underestimation at finite, small system sizes.

As expected, $T_2$ scales linearly with the system size for $h\gtrsim h^*_2$ and logarithmically for $h\lesssim h_2^*$.
Moreover, the curves in Fig.~\ref{fig2sp} peak on a system-size-dependent value $h_2^*(N)$.
In Fig.~\ref{fig:peaksp} we show the scaling of the $T_1$ and $T_2$ peak positions with the system size.
For both the $T_1$  and $T_2$ peak positions, the finite-size scaling is very well approximated by a linear behaviour in $1/N$; the infinte-size extrapolation for the $2$-Renyi case is $h^*_2(\infty)=3.6\pm0.2$, which is lower than the value obtained from the Von Neumann total correlations. This is again a signal of the underestimation of the breaking of ergodicity and of stronger finite size effects due to the hierarchy in the Renyi entropies.

\begin{figure}
\includegraphics[width=1\columnwidth]{{fig2sp_am_delta1.}.pdf}
\caption{(Color online) The $2$-Renyi total correlations of the diagonal ensemble, starting with a Neel state, for the Heisenberg model with random fields (whose Hamiltonian is Eq.
\eqref{eq:mbl} with $h_i\in[-h,h]$ and $J_x=J_y=J_z=1$), rescaled with the system size. The markers on the top axis denote the positions of the local peak $h^*(N)$, excluding the case $N=8$, where no local maximum can be discerned.
The curves show a system-size-dependent peak (see Fig.~\ref{fig:peaksp}) and collapse for $h\gtrsim2$.
\textit{Inset.
} System size scaling of the total correlations for three example values of $h$, showing a logarithmic scaling deep in the delocalized phase and a linear scaling for disorder values near the transition (which is at $h_c\approx3.7$) and in the localized phase.}
  \label{fig2sp}
\end{figure}

\begin{figure}
\includegraphics[width=1\columnwidth]{{fig3_tc2_aam_delta1.}.pdf}
\caption{(Color online) The $2$-Renyi total correlations of the diagonal ensemble, starting with a Neel state, for the Aubry-Andr\'e model (whose Hamiltonian is Eq.
\eqref{eq:mbl} with the cosine $h_i$ fields and $J_x=J_y=J_z=1$), rescaled with the system size.
The curves show a system-size-dependent peak (see Fig.~\ref{fig:peaksp}) and collapse for $h\gtrsim 3$.
\textit{Inset.
} System size scaling of the total correlations for three example values of $h$, showing a logarithmic scaling deep in the delocalized phase and a linear scaling in the localized phase.}
  \label{fig:tc2aam}
\end{figure}

Finally, in Fig.~\ref{fig:tc2aam} we show the results for the $2$-Renyi total correlations of the Aubry-Andr\'e model. The qualitative behaviour is again the same as for the model with random fields, showing once again that the interactions remove the special integrability features of a non-interacting Aubry-Andr\'e model.  Specifically, $T_2(\omega)/N$ has a peak which scales to $h_2^*(\infty)=3.5\pm0.6$, which, analogously to what happens in the random fields model, is a lower value than the result for the extrapolated peak of the rescaled Von Neumann total correlations.

\begin{figure}
\includegraphics[width=1\columnwidth]{{peak_sp}.pdf}
\caption{(Color online) System size scaling of the peak of the total correlations in the Heisenberg model with random fields, for both $T_1$ and $T_2$.
The peak is extracted from a polynomial interpolation of each of the curves in Figs.~\ref{fig2} and \ref{fig2sp}, in which it is denoted with a marker on the top axis.
We perform a linear fit in $1/N$ and obtain the infinite size extrapolation given in the text.}
  \label{fig:peaksp}
\end{figure}

\section{Conclusions}
The results displayed in this work demonstrate that the total correlations of the diagonal ensemble is a powerful concept to understand ergodicity breaking in quantum systems in general.
The numerics performed in different models confirm that the scalings predicted in the theory first outlined in \cite{Goold:2015} work in the cases of both integrability breaking and also ergodic to MBL transitions.
Within the context of systems which show ergodicity breaking, a number of methods have proven useful, especially in the case of localizable systems, consisting in examining the participation ratio~\cite{de2013ergodicity}, the entanglement entropy~\cite{Bardason2012} and the full entanglement spectrum~\cite{entspect2016}. The total correlations presented here are an additional tool for such systems.
Where MBL systems are concerned the rescaled quantity offers the additional feature of peaking around the expected transition point; given that this may be seen as a divergence of correlations in the infinite time steady state, it represents a novel contribution to the theory of quantum correlations. The peak was observed in two models displaying a MBL transition.

We have examined the total correlations \eqref{eq:totcor1} for two values of $\alpha$, $\alpha=1$ and $\alpha=2$; the $2$-Renyi total correlations has the numerical advantage, being more suitable to be computed avoiding the diagonalization of the density matrix through faster techniques such as t-DMRG, where a finite time average could be performed.
As future work we intend to increase the system sizes dramatically by applying t-DMRG and finite time averaging to compute the $2$-Renyi total correlations.

Finally, given the rapid progress in experimental techniques it seems possible that the total correlations could be experimentally measured in the near future.
The total correlations amounts to subtracting the diagonal entropy from the sum of the entropies of the marginal states.
The marginal states and their entropies can already be measured in a quench starting from a Neel state \cite{Smith:2016}.
Measuring the diagonal entropy is a more challenging task, however, some progress has been made in this direction for small systems \cite{Neill:2016} and given the current interest in measuring Renyi entropies in experiments \cite{Islam:2015} we believe that further advances could yield the experimental extraction of total correlations.

\section*{Acknowledgements}
FP would like to thank G. Parisi for useful discussions and SISSA and ICTP for access to computing resources and hospitality during the completion of this work.
CG acknowledges support from MPQ-ICFO, ICFOnest+ (FP7-PEOPLE-2013-COFUND), and co-funding by the European Union's Marie Sk\l{}odowska-Curie Individual Fellowships (IF-EF) programme under GA: 700140, as well as from the European Research Council
(ERC AdG OSYRIS and CoG QITBOX), Axa Chair in Quantum Information Science,
The John Templeton Foundation, Spanish MINECO (FOQUS
FIS2013-46768 and Severo Ochoa Grant No.~SEV-2015-0522),
Fundaci\'{o} Privada Cellex, and Generalitat de Catalunya (Grant No.~SGR 874 and 875).

redpajama_set_name: RedPajamaArXiv


"Home style chicken noodle soup that really makes a wonderful side or meal, it cures what ails you. If you like lots of noodles use a whole pound of them. Serve hot with your favorite salad and bread. This freezes or doubles well."
See how to make an amazing homemade chicken noodle soup.


For the first time, the Department of Health and Social Care has published statistics on preschool children with mental health conditions.
Findings from the 2017 prevalence survey show that one in eighteen two- to four-year-olds has a condition that meets diagnostic thresholds – which, by definition, causes them significant distress or impairs their functioning. These consist mainly of behavioural disorders, autism spectrum disorder and conditions specific to very early life, including sleeping or feeding problems.
This is low compared to older age groups. For boys, the prevalence of disorders peaks at 14 per cent in 11- to 16-year olds, and for girls, at a striking 24 per cent in ages 17 to 19. As the survey authors note, it can be difficult to identify issues in this very young, and rapidly developing, age group. In addition, prevalence in preschool children is based solely on parental report of symptoms – whereas input from teachers and children themselves at older ages helps to paint a clearer picture of problems.
Despite this, policy-makers should be wary of overlooking very young children – for several reasons.
The overall figure masks substantially higher prevalence in some groups of vulnerable children. Similar to older children, parental mental health is a key risk factor: conditions are more than three times more common in children with parents suffering from difficulties themselves. Lower income children are more than twice as likely to be affected compared to their more affluent peers, with boys from white ethnic backgrounds also at higher risk. One in ten children in the North were identified with a condition compared to only 3 per cent in the South East, and 5 per cent in London and the Midlands and East respectively.
Moreover, these findings follow anecdotal reports of rising incidence of self-harm among children as young as three. The vast majority of lifelong mental health conditions develop in childhood and adolescence, and adverse experiences in very early life have lasting negative consequences for health, attainment and income potential.
EPI's recent report on the state of child and adolescent mental health services in 2018 found that approximately a quarter of all children referred to specialist services are turned away – with wide variation across the country – mainly because they do not meet eligibility criteria. Our previous research has highlighted that children with complex issues often do not fit into diagnostic boxes, which can result in those most in need of support missing out; the complexities around diagnosing problems in very young children may exacerbate this risk. Added to this, the significant reduction in child and family early intervention services over the last eight years means that children with lower-level needs may not be able to access help in some areas.
Effectively addressing mental ill health in children requires an up-to-date understanding of the scale of difficulties. These statistics provide a starting point.
Yet more research is required into how emotional ill health presents in very young children, as well as the impact of conditions in this period on later life outcomes. We need a better understanding of the number of children with mental health needs who do not meet diagnostic thresholds.
This should be coupled with concerted action to tackle the known risk factors for poor mental health in children of all ages. It is widely accepted that prevention and early intervention are best, both for the well-being of those with difficulties and because of the much higher cost of acute treatment; addressing mental ill health in this very young age group is likely to reduce the significantly higher prevalence we see in older children.
An effective strategy must include policies that create and support the conditions for healthy child development and positive early life experiences. The NHS has committed to rolling out mental health services to expectant and new mothers and fathers – a positive first step in addressing one of the key contributors to children's mental health.
 These are experimental statistics, defined as official statistics published to involve users and stakeholders in their development, and to introduce quality at an early stage.


As your baby grows, his/her nutritional needs change. You can select suitable recipes here, depending on your baby's age.
Important: Always remember that you should never sweeten baby food with honey or maple syrup!
Both of these may contain germs which generate poisons in your baby's bowels, leading to infant botulism. This results in gradual paralysis of all muscles.
In older children and adults, the intestinal flora prevents the formation of this poison.
Vary the type of vegetable (pumpkin, carrots, turnip cabbage, broccoli, cauliflower, courgette) and see how your baby reacts to each of them.
Clean the vegetables and peel the potatoes.
Finely chop the potatoes and vegetables and cook them in a little water until they are soft ‒ ideally using a steam cooker.
Purée the vegetable and potato mix and stir in the oil. If the purée is too firm, add a little water.
To provide variety, select different types of vegetable (pumpkin, carrots, turnip cabbage, cauliflower, broccoli, courgette).
Finely chop the potatoes, vegetables and meat and cook them in a little water until they are soft ‒ ideally using a steam cooker.
Purée the vegetable, potato and meat mix before stirring in the oil and fruit juice. If the purée is too firm, add a little water.
Studies have shown that getting your baby used to fish early on prevents allergies. Fish should therefore appear on the menu 1 x per week. Combine this with various types of vegetables such as pumpkin, carrots, turnip cabbage, cauliflower, broccoli or courgette.
Finely chop the potatoes, vegetables and fish and cook them in a little water until they are soft ‒ ideally using a steam cooker.
Purée the vegetable, potato and fish mix and stir in the oil. If the purée is too firm, add a little water.
Important: Thoroughly ensure that there are no absolutely bones in the fish!
Add the milk to the cereal flakes or semolina and bring to the boil.
Leave it to stand for a few minutes.
Then stir in the fruit juice or puréed fruit (e.g. mashed banana or apple/pear that has been grated using a glass grater).
Stir the cereal flakes into the water, bring to the boil and leave to stand.
Mash a banana or grate an apple or a pear using a glass grater.
Stir the fruit and oil into the cereal flakes. Add water if necessary.


A wide set of optical sources is available with different specifications and characteristics. On the one hand, a tunable optical source in the O band (from 1260 to 1360 nm), several tunable optical sources in the S, C and L bands (from 1460 to 1625 nm), a tunable optical source which combines high output power (more than 10 dBm) with ultra-low Source Spontaneous Emission (SSE) and an array of 40 tunable optical sources spaced 0.8 nm each other in the C band. On the other hand, Amplified Spontaneous Emission (ASE) broadband light sources with output powers up to 20 dBm in the C and L bands, pulsed lasers, high power Argon and Helium-Cadmium lasers.


Look super cute in this gorgeous dress! Dresses are a piece that suits absolutely everyone and our team are completely obsessed with them and feel you can never have too many. This item is now available for express shipping. Shipping free shipping over $75 on australian orders. For all other info about shipping times and costs please check our faq page.


Parents could hire and fire principals with school councils given unprecedented powers under a proposed shake-up of Victoria's public education system.
In a move that has been met with caution from teachers and principals, the state government is conducting a sweeping review into the role of school councils amid growing fears too many students are falling behind, partly because of ineffective governance.
Education Minister Martin Dixon wants more decisions such as staffing arrangements and subject specialisation to come ''from the bottom up'', through governing boards with higher levels of business and community expertise. Struggling public schools could end up sharing the same super council with high-performing neighbouring schools, similar to Britain's ''federated'' schools model.
And in a contentious policy shift, school councils - made up largely of parents - could get full power to employ and sack the principal, manage his or her performance, and ''be more flexible in determining teacher career structure within the school''. At present, the Education Department is the main employer.
In Victoria, school councils comprise parent and teachers, and can also include student representatives and business and community leaders. Collectively, they have three broad responsibilities: overseeing the school budget, strategic planning, and implementing school policies.
Australian Education Union state president Meredith Peace said the current system generally worked well, but giving councils authority to hire and fire could lead to favouritism or risk principals being sacked because of personality clashes with school council members.
Frank Sal, president of the Victorian Association of State Secondary Principals, warned that while schools would not object to the review, ''we are certainly against change for change's sake, or change that is merely politically inspired''.
Mr Dixon has set up a reference committee and a discussion paper flagging the proposed changes will be released next month. The review is based on the belief that the quality of school councils can be a ''major contributor'' to students' results.
Mr Dixon said Australian schools were falling behind those in other economies and something had to give.
''To make our schools international top-tier schools, one of the basic changes we've got to make is to ensure change is coming from below, and that it's not a 'top-down' approach. We want schools to really reflect their community and meet the needs of the local community,'' he said.
Nicholas Abbey, president of the Victorian Council of School Organisations, said the review would provide an opportunity to work out if school councils were ''getting the right mix'' of parents and community members.


Following on from her 2016 Small Development Project Trust me! Academic leadership behaviours in creating 'quality' doctoral supervision relationships, Kay Guiccione examines in this report the range and reach of the role of PGRT in close detail. In particular, it uses the narratives of those who have taken up the role to document its challenges. Examples of good practice and imagined 'better ways' are combined in this study to spark the imagination of those in higher education institutions to discuss how the role can be understood, positioned, communicated, and the PGRT be properly supported to achieve.


Convert RAW digital photos (and JPEG and TIFFs, too!) into beautiful images with SILKYPIX DS Pro9.
SILKYPIX DS Pro9 for macOS and Windows has hundreds of features for correction and conversion of your photos into breathtaking images.
Your SILKYPIX DS Pro9 license includes the right to install on up to three computers in any combination of macOS and Windows operating system computers (this is why license is N/A).
Upgrade options are only visible to logged in customers that registered their products with us or purchased from us.


We are looking for someone to help us create an app that teaches developers to stop selling apps for free. Selling free apps is making everyone expect apps to be free and is only benefiting the mobile phone companies.
Developers usually don't have business skills and make everything free to feel good. This is bad and the app we are writing will try to make every developer change their minimum app price so we can all make money.


Accessing information and updates on student loans just got easier with the introduction of a toll-free phone number. Joan Burke, minister of Education, said that improvements to the system mean when students call during regular work hours to speak with a student aid representative, they can do so free of charge.
"Prior to this, the toll-free line simply provided access to the automated system," said Minister Burke. "If students wanted to speak to someone at the student aid office, those outside the St. John's area incurred long-distance charges. This was an onerous, and I believe unnecessary, expense.
Improving the toll-free service at the student aid office was made possible through investments made in the 2008 provincial budget. More than $280,000 was provided to improve services to students under the student aid program, part of the additional $27 million allocated for the post-secondary education system this year.
To speak to a student aid representative, students can call toll-free 1-888-657-0800. Students are also encouraged to continue to use other available services such as e-mail (studentaid@gov.nl.ca), web-based services (www.gov.nl.ca/studentaid) or visit the student aid office located in Coughlan College on MUN campus.
Nominations are currently being solicited for the next Galbraith Lecturer. Members of the Memorial University community, as well as of the community at large, are invited to submit the names of individuals with a national or international reputation, who, could deliver a lecture on a topic of public policy.
The most recent Lecturer was Geir Haarde, Prime Minister of Iceland. Previous lecturers included Margaret MacMillan, author of Nixon in China and 1919: Six Months that Changed the World; Ken Carty of the University of British Columbia, an expert on electoral reform; and Jeffrey Simpson of the Globe and Mail.
Nominations should contain the name of the proposed speaker and a one-page brief on why this is an appropriate choice. The nomination should also include the name and contact information of the nominator. The deadline is Friday, Aug. 8, and nominations should be addressed to the Harris Centre at mclair@mun.ca.
More information is available about the Galbraith Lecture by visiting the Harris Centre's website at www.mun.ca/harriscentre/Galbraith_home.php.
After eight seasons at the helm of Memorial's men's basketball team, Todd Aughey has resigned as head coach last month. Mr. Aughey cited a desire to explore new opportunities as the reason for the decision.
He also indicated that he feels that the program will benefit from new leadership at this time.
Michelle Healey, director of Athletics at Memorial, indicated that Mr. Aughey's dedication and commitment to the program was exemplary.
Memorial immediately began the process to initiate a search for a new men's basketball head coach.


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Billy J. Kramer: Life With Billy J.!. By Peter Jones : Articles, reviews and interviews from Rock's Backpages.
BILLY J. KRAMER lashed back his second entire French loaf, whooshed amiably through a large crab salad — and talked about the trials, tribulations and joys of being a top pop-seller.


text:
Q: Make a pdf out of a Vue.js component that is not rendered in the router-view I have a website with a permanent button for people to download a pdf document (my CV). Permanent meaning that it's present on the nav-bar of the website at all times for people to download it.
But I want to control what is included in the pdf, so I decided to create a new component, named MyCV and use json documents to dynamically build the html that will be eventually extracted to pdf.
So I approached this problem like so:

*

*Add the new component MyCV to App.vue

*Hide the component with v-show="false" because I don't ever want it to be seen

*On click on the Download button, trigger a custom event exportpdf, which will be picked up by MyCV component and which will trigger the actual export to pdf function.

It sounds very simple and logical in theory, but in practice it's not working (or I may be very rusty when it comes to Vue.js).
The code:
App.vue
<template>
...
   <v-btn small v-on:click="emitExtractPDFEvent()">Download CV</v-btn>

...

   <MyCV
       v-show="false"
       v-on:extractpdf="printToPDF()"
   ></MyCV>
</template>

<script>

      emitExtractPDFEvent: function() {
          this.$emit('extractpdf');
      },
      printToPDF: function() {
        console.log('MAGIC! I'm ready to export the pdf!!!');
      }
</script>

This is definitely not caused by html2canvas or jspdf, as I stripped the method of any html2canvas/ jspdf code just to make sure I got everything right with the whole custom event first.
Thanks in advance!

A: I ended up trying to rephrase the problem and got to this question and answer: How to call function on child component on parent events
I gave up the whole custom event solution and simply ended up triggering the print to pdf method present in the child component from the parent, when the click event is fired.

A: You can only generate PDF (printable) of the content that is being displayed on the page. What actually happens is chrome converts the view to an image that can be printed this can be done by using the window.print() function but it will not work until the content is displayed on the screen.
For generating PDF out of json data and without showing it to user, i will recoment you to check some third party libraries like jsreport

redpajama_set_name: RedPajamaStackExchange


text:
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Episode 9 – Bird insurrection
Cardinal in Margaret's birdbath. Photo copyright 2021 by Richard Creps.
Richard and his daughter Margaret investigate the bird insurrection, while humans attack the U.S. Capitol and President Trump is impeached for the second time.
Birds provide joy, humor, and solace in rough times, and it seems that they share the capacity for feelings with the human species. And boy, are there a lot of feelings swooping and fluttering around right now!
Margaret is struggling with a loss of faith in her fellow humans. She pulls an old recording from 2012 in which Richard describes his encounter with the American eagle, and Eunice, Margaret's mother and Richard's wife, joins him in singing his favorite hymn, "The Lone Wild Bird."
In loving memory of Eunice Blanchard Poethig, 1930-2018.
What It's Like to Be a Bird, by David Allen Sibley: https://www.sibleyguides.com/product/what-its-like-to-be-a-bird/
Loren Eiseley: https://en.wikipedia.org/wiki/Loren_Eiseley
Music Credits:
An Unknown Visitor by Blue Dot Sessions
"The Lone Wild Bird," by Henry Richard McFadyen: https://hymnary.org/text/the_lone_wild_fowl_in_lofty_flight
Cardinal in Margaret's birdbath by Richard Creps
Keeping Dad Alive
Conversations between a dad and his children capture the sheer joy of talking, singing, and laughing with Richard, a man of simple pleasures, expansive intelligence, historical perspective, and progressive politics. In Season 1, Richard is living under lockdown in his senior living residence during the coronavirus pandemic. It tells the story of Richard's resilience and of the family's efforts to ease the psychic impact of his isolation. In Season 2, Margaret asks Richard why he talked so much about vocation when she was growing up. Richard offers the wide arc of his theological understanding—from the need to care for working people to the cosmic Spirit that holds the universe together. They decided to devote an entire podcast season to vocation.
byMargaret Poethig
In loving memory of Eunice Blanchard Poethig, 1930-2018
An Unknown Visitor by Blue Dot Sessions: https://www.sessions.blue/
© 2021-2022 Margaret Poethig
If you'd like to be notified by email when new episodes are posted, please sign up here.

redpajama_set_name: RedPajamaCommonCrawl


text:
Herman Kountze (August 21, 1833 – November 20, 1906) was a powerful and influential pioneer banker in Omaha, Nebraska, during the late 19th century. After organizing the Kountze Brothers Bank in 1857 as the second bank in Omaha, Herman and his brothers Augustus, Charles and Luther changed the charter in 1863, opening the First National Bank of Omaha that year. Kountze was involved in a number of influential ventures around Omaha, including the development of the Omaha Stockyards and the Trans-Mississippi and International Exposition of 1898.  Immediately after his death Kountze was regarded as one of Omaha's "old settlers". Today Kountze's First National Bank is the oldest bank west of the Mississippi River, and continues as a privately held company in its sixth generation of family ownership.

Biography
Herman Kountze was born August 21, 1833, in Osnaburg, Ohio, one of twelve children born to Christian and Margaret Kountze. After leaving his father's mercantile business at the age of 26, Kountze moved to join his brother Augustus, who was a real estate agent in the new Omaha City, located on the eastern edge of the Nebraska Territory. Immediately the brothers organized the Kountze Brothers Bank and bought a large amount of land in the river towns along the Missouri River in Nebraska, with holdings in Brownville, Nebraska City, Tekamah, and Dakota City, and in Sioux City, Iowa. Eventually they invested throughout Nebraska, across Iowa, Minnesota, and the forests and grazing lands of east Texas, as well as in Chicago and Denver. In 1864, Kountze married Elizabeth Davis, the daughter of Thomas Davis, a founding pioneer of Omaha. In 1899, after his first wife died, he was married for a second time to Clara Sara Whitney Cotton.

Kountze Brothers Bank

In 1867, Herman joined his brother in organizing the First National Bank of Omaha, with fellow Omaha businessman Edward Creighton serving as the first president. Herman was the bank's first cashier, and became the second president of the bank after Creighton died in 1873. In 1862 he joined several of his brothers, including Augustus, in founding the Kountze Brothers Bank of Denver, which became the Colorado National Bank in 1866.

Herman's brother Luther went to New York City and founded the Kountze Brothers Bank there in 1867. Herman joined his brother Augustus as senior partner, and by 1872 Augustus moved permanently from Omaha to New York to manage affairs directly. After Augustus left, Herman took the management of the affairs of the firm in Nebraska, Iowa and Minnesota.

Other ventures
Herman Kountze was a prolific investor. Among his holdings were a number of railroads, including the Omaha and Northwestern Railroad, the Denver and South Park Railroad, the Sabine and East Texas Railway, the Boston, Hoosac Tunnel and Western Railway, and the Troy and Boston Railroad.

In 1872, while misunderstanding the ideal location he was selling, Kountze sold the land required to develop Neligh, Nebraska, which eventually became the county seat of Antelope County.

In 1883 Kountze was a plaintiff and defendant in a lawsuit and counter-suit with the Omaha Hotel Company owned by John J. Reddick. The case pertained to the money owed in a failed real estate investment scheme. Other codefendants in the case included other pioneer investors in Omaha: Jeptha H. Wade, James W. Bosler, Thomas Wardell, Henry W. Yates and John A. Creighton. They were represented by pioneer lawyer Andrew J. Poppleton.

In 1895 Kountze helped found the Knights of Ak-Sar-Ben to promote Omaha business interests. Its first meeting place was in North Omaha at North 20th and Burdette Streets, located in Kountze Place.

North Omaha

Aside from the aforementioned Kountze Place, Kountze dealt in a great deal of land throughout North Omaha. He sold an  tract of land four miles (6 km) north of Omaha and 1½ miles south of Florence to the U.S. Army in 1868. It became Fort Omaha. In the late 19th century he donated land to the Sacred Heart Church at 2206 Binney Street. Kountze donated land to Brownell Hall to relocate from the former town of Saratoga to South Tenth and Worthington Streets in the late 19th century.

Trans-Mississippi Exposition

Herman Kountze was the treasurer for the Trans-Mississippi Exposition of 1898. After running into transportation issues with its first land choice for the event, Kountze volunteered to sell part of his Kountze Place development to the city. As part of the real estate transaction, the City used a small parcel to develop Kountze Park, which still functions as a neighborhood park in that area.

Creighton University

Working with John A. Creighton, Herman Kountze was an executor of the will of Mary Lucretia Creighton after her death in 1876. In that capacity he was partly responsible for carrying out the original intentions of Edward Creighton, Mary's husband, who wanted to found a free university in Omaha. That institution eventually took the shape of Creighton University.

Omaha Stockyards

Kountze was a partner in the South Omaha Land Syndicate, the South Omaha Land Company, and the Union Stock Yards Company of Omaha of South Omaha. This company was responsible for building the Union Stockyards and the Livestock Exchange Building, and ran the South Omaha Terminal Railway.

Kountze, Texas

The city of Kountze in Hardin County, Texas was named in honor of Herman and Augustus. They were early financial backers of the Sabine and East Texas Railroad which established the town as a station on the line. As retail businesses and lumbermen accompanied the railroad, the town of Kountze grew, and in 1886 the town became the county seat.

Death
Herman Kountze died in 1906 and was interred in Omaha's Forest Lawn Cemetery, of which he was a founding trustee and in which there is a roadway named for him.

See also
 History of Omaha
 Founding figures of Omaha, Nebraska

References

External links
 Historic image of Herman Kountze
 Historic image of Kountze when he was older.
 Historic images of Herman Kountze's residence in Omaha - Nebraska Memories

Bibliography
 Szmrecsanyi, S. (1996). The First National Bank Story. Omaha, NE: First National Bank of Omaha.

1833 births
1906 deaths
People from Stark County, Ohio
American bankers
American real estate businesspeople
South Omaha, Nebraska
Herman
Businesspeople from Omaha, Nebraska
Meatpacking industry in Omaha, Nebraska

redpajama_set_name: RedPajamaWikipedia


Breast meat chicken skewed in tandoor and sauteed in tomato & rich creamy sauce topped with bell peppers.
2 pcs Crispy triangular pastry turnovers filled with seasoned potatoes and green peas.
Pulled chicken cooked in tandoor and sauteed in special buttery tomatoes and rich cream sauce.
Tender pieces of chicken sauteed with Indian herbs cooked in spinach. Served with saffron bashmati rice.
Chickpeas Garbanzo beans cooked in a special blend of traditional spices.
Sweet cottage cheese dumpling with saffron & cardamom.
Saffron basmati rice cooked with goat with bones, topped with fried onions and herbs.
A thin crisp lentil flour cooked in the clay oven.
Assorted fried vegetables frittes. Includes cauliflower, onion, potato and spinach.
Mixture of crisps, potatoes, and chickpeas in a yogurt and tamarind & mint sauce.
Combination of assorted vegetable samosa, mixed pakora, and paneer pakora.
Fresh cauliflower with cubes of bell peppers, spring onion slightly sauteed and tossed with Manchurian sauce and garnished with fresh cilantro.
Veggie samosa with mildly spiced chickpeas, potatoes, onion, tomato and garnished with yogurt, tamarind and mint sauce.
Cottage cheese dipped in gram flour batter with Indian spices and deep fried to perfection.
Cottage cheese battered with cornstarch, sauteed with bell peppers, chili paste spring onions, and blend of soy sauce.
Crispy triangular pastry turnovers filled with minced lamb seasoned with potatoes and green peas.
Cubes of chicken breast sauteed with chili paste, soy sauce, onions, bell peppers, herbs and exotic spices.
Toasted fish marinated in chili paste with cubes bell pepper and house spices.
Fresh shrimp tossed in roasted garlic and cooked in vinaigrette bell peppers and rich cream.
Batter fried coconut flavored filet of chicken served with mango chutney.
Combination platter of chicken seekh kabab, chicken malai kabab, lamb samosa and chicken tikka.
Cucumber, tomato, red onion, and mint.
Punjabi north Indian dish made of mustard leaves cooked with spices in butter.
Special preparation of cut tossed okra with diced onions, tomatoes, and traditional spices.
Black lentils cooked overnight on a very slow fire flavored with butter, creamy sauce & spices.
Eggplants roasted over charcoal with fresh tomatoes, peas, ginger, garlic and onions seasoned with herbs.
A medley of nine vegetables cooked with mild creamy sauce with cashews and raisins.
Spinach and chickpeas Garbanzo beans cooked with thick gravy sauce.
homemade vegetables balls cooked in a mildly spiced creamy sauce with cashews & raisins.
Combined seasonal vegetables cooked in house blended curry sauce. Serve with saffron basmati rice.
Cubed potatoes and cauliflower cooked with spices and herbs. Serve with saffron basmati rice.
Cottage cheese sauteed with tomato, onion, pepper, and herbs.
Traditional mughalai offering. Boneless chicken cooked in heavenly curry sauce, seasoned to your taste.
A Mughulai delight Cardamoms flavored sweet and spicy curried chicken in cream, cashews, and raisins.
Boneless chicken cooked with fresh onion, tomatoes and house spices.
Boneless chicken sauteed with special ginger sauce, bell peppers, onion & fresh tomatoes along with herbs and spices.
Cubes of chicken breast sauteed with chili paste, soy sauce, onions, bell peppers green chilies, herbs and exotic spices.
Boneless chicken sauteed with natural methi leaf, onions and tomatoes and special spices.
Pieces of chicken cooked with coriander sauce, mint and blend of spice. Served with saffron bashmati rice.
Cube chicken cooked with fresh mix vegetables along with homemade sauce.
Chicken cooked with roasted coconut, mustard seed, and hot chili pepper.
Chicken leg quarters marinated in yogurt, fresh spices and lemon juice then barbecued in the clay oven.
Cubes of chicken breast marinated in yogurt, herbs, and spices then cooked on skewers in the clay oven.
Ground minced chicken mixed with onion, ginger, and herbs.
Ground minced lamb mixed with onion, ginger, and herbs.
Chunks of salmon marinated in yogurt, herbs, and spices then barbecued in the clay oven.
Combination platter of tandoori - Chicken Tikka, Chicken Seekh Kebab, Lamb Seekh Kebab, Shrimp & Fish.
Salmon fish cooked in a hearty blend of tangy tomatoes, onions and aromatic herbs and spices.
Shrimp cooked with potatoes in a special and tangy vinaigrette sauce.
Shrimp cooked with fresh spinach, spices, and ginger.
Shrimp cooked in clay oven sauteed with tomatoes, green pepper, and onion in a rich creamy sauce.
Shrimp cooked with fresh tomatoes, green peppers, ginger, spices, and herbs.
Bone in goat marinated and cooked in a curry sauce of fresh herbs and spices.
Bone in goat sauteed with special ginger sauce cooked in herbs and spices.
Bone in goat cooked with potatoes in a spiced and tangy vinaigrette sauce.
Bone in goat sauteed with exotic seasoned spinach and fresh herbs.
Boneless tender pieces of lamb cooked with onions, Garlic & ginger in fresh herbs and spices.
Boneless lamb sauteed with special ginger sauce, bell peppers, onions & fresh tomatoes along with herbs and spices.
Boneless lamb cooked with potatoes in a spiced and tangy vinaigrette sauce.
Tender pieces of lamb cooked with onions, garlic & ginger in fresh herbs and spices.
Cardamoms flavored sweet and spicy curried lamb in cream, cashews, and raisins.
Tender lamb cooked in exotic blend of cream, almond sauce, and spices.
Boneless tender lamb cooked in tandoor and sauteed in a rich creamy and tomato sauce with bell peppers.
Juicy boneless Beef cooked with Basmati Rice & traditional spices.
Boneless tender pieces of beef cooked with onions, garlic, & ginger in fresh herbs and spices.
Boneless beef cooked with special ginger sauce, bell peppers, onions & fresh tomatoes along with herbs and spices.
Boneless beef cooked with potatoes in a spicy and tangy vinaigrette sauce.
Boneless beef sauteed with exotic seasoned spinach and fresh herbs.
Boneless tender pieces of beef skewed in Tandoor (Clay oven) and sautéed in rich creamy & tomatoes sauces with bell peppers.
Stuffed with mozzarella cheese and garlic.
Combination of breads. Plain naan, onion naan, and garlic naan.
Yogurt with cucumber, carrot, tomatoes, onion, and herbs.
Well brewed spiced ice tea.
Fresh squeezed sweet lemon drink.
Most popular puritan flavor, made with premium vanilla extract.
A rich chocolate ice cream made from scratch with premium cocoa.
Indian homemade fresh mango ice cream.


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Peru opens corruption probe into ex-President Toledo
FILE - In this March 17, 2011 file photo, Peru's former President Alejandro Toledo campaigns for reelection at the Santa Anita wholesale market in Lima, Peru. Peruvian authorities said they searched Toledo's house on Saturday, Feb. 4, 2017 in a case involving alleged bribes from a construction firm under investigation in a major corruption probe in Brazil. Toledo currently is in Paris and denied the charges by telephone to Peruvian media. (AP Photo/Karel Navarro, File) (The Associated Press)
LIMA, Peru – Prosecutors in Peru are opening a formal investigation into suspicions that former President Alejandro Toledo took bribes from a Brazilian construction firm at the heart of a major corruption scandal shaking politicians across Latin America.
The move comes after police on Saturday searched Toledo's home in Lima. The former president is not in Peru but has denied any wrongdoing.
Authorities are looking into whether some $29 million in bribes paid by the construction firm Odebrecht ended up in Toledo's hands.
Odebrecht acknowledged in a plea agreement with the U.S. Justice Department that it gave some $800 million in bribes to win business in 12 countries, including to officials in Peru during Toledo's administration. Toledo became president in 2001 after leading protests that toppled strongman Alberto Fujimori.


text:
Q: Nodejs outbound HTTP requests delayed despite high maxSockets I am developing a node.js app locally on Mac OS X 10.9.5 that proxies requests for large files on another server. I have tried writing my app using node-http-proxy, and also with a simple http/request one-liner (req.pipe(request()).pipe(res)). Both work fine until I start making e.g. 30 simultaneous requests to my proxy for a large-ish(90MB) file. Tailing the access log on the backend server, I can see that only a portion of my proxied requests appear immediately. The others trickle in many seconds and sometimes minutes later. In some cases, the later outbound requests correspond with the completion of some of the requests that arrived immediately, and in other cases I see no patterns as far as what is unblocking the requests. The number of requests that make it out to the backend server immediately is inconsistent. I have tried setting http.globalAgent.maxSockets to a number much larger than my 30 requests, but this does not make a difference. Any other ideas as to what could be delaying a subset of my outbound HTTP requests?? Thanks!

A: Note that there are (at least) two outbound HTTP socket pools.  You have properly configured the one for outbound http connections using, http.globalAgent.maxSockets, however, there is another one for https connections, https.globalAgent.maxSockets.
And just as a refresher.  From the node docs on the matter:

agent.maxSockets#
By default set to 5. Determines how many concurrent sockets the agent can have open per origin. Origin > is either a 'host:port' or 'host:port:localAddress' combination.


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text:
Gear Envy: Inside the Bag of PCMag's Camera Expert
Our resident photography ace and camera reviewer, Jim Fisher, switches up his kit frequently—what's he shooting with this week? Let's take a look.
https://www.pcmag.com/picks/gear-envy-inside-the-bag-of-pcmags-camera-expert
Table of Contents Table of Contents Return to The Top Think Tank Signature 13 Sony a7R III Sony FE 100-400mm F4.5-5.6 GM OSS Sony Zeiss Planar T* FE 50mm F1.4 ZA Think Tank SD Pixel Pocket Rocket 13-Inch MacBook Pro Sony Card Reader Apple iPhone 8 Plus B&W C5 Headphones Lumu Power
Despite our name, PCMag focuses on more than just computers. I'm Jim Fisher, and I cover the digital photography space, reviewing scores of new cameras and just as many lenses every year. Because of this, I've got a different camera in my bag almost every week, ranging from entry-level mirrorless models to pro-grade SLRs .
This week I'm working with a new camera from Sony, a high-resolution full-frame monster with exceptional image quality and quick autofocus. Next week it'll be something different, maybe a consumer-friendly SLR from Canon or Nikon, or a tough point-and-shoot from Olympus.
Let's take a look inside my bag, both at the camera and other items I carry.
Think Tank Signature 13
$279.75 at Amazon
I have too many camera bags, a common problem among photographers. But my daily driver is the Signature 13 ($279) from Think Tank Photo. It's attractive, with a slate gray finish and brown leather accents, and spacious inside, without being too bulky to use for a public transit commute.
Sony a7R III Mirrorless Camera
$2,798.00 at Amazon
I just finished my review of the Sony a7R III, the company's high-resolution full-frame mirrorless model. It packs a 42MP image sensor and shoots video in 4K, offers in-body stabilization, and has much faster tracking, continuous shooting (10fps), and a larger battery than the older a7R II. It's shown here with the FE 12-24mm F4 G lens attached.
Sony a7R III Review
Sony FE 100-400mm F4.5-5.6 GM OSS
I don't shoot a lot of sports, but I do enjoy photographing nature and wildlife. The FE 100-400mm F4.5-5.6 GM OSS is currently the longest lens available for the Sony system, and delivers excellent image quality, even if it doesn't have the brightest aperture. It doesn't have the reach of my favorite telezoom, the Sigma 150-600mm Contemporary, but unlike the Sigma it fits in this bag and works with the Sony system without the need for an adapter.
Sony FE 100-400mm F4.5-5.6 GM OSS Review
Sony Zeiss Planar T* FE 50mm F1.4 ZA
I love shooting with a standard-angle prime. The Sony Zeiss Planar T* FE 50mm F1.4 ZA is one of the best you can get for the Sony system. It blurs backgrounds with aplomb, focuses quickly, and delivers very sharp images.
Sony Zeiss Planar T* FE 50mm F1.4 ZA Review
Think Tank SD Pixel Pocket Rocket
You can never have too many memory cards. The SD Pixel Pocket Rocket is a wallet that holds nine SD cards. It's also got a larger front pocket that I can use to hold a CF, CFast, or XQD card when I'm shooting with a camera that doesn't use SD.
Apple MacBook Pro 13-Inch (2017, Touch Bar)
I'm a Mac guy, have been for years. I like to pack on the lighter side, so I decided to sacrifice some screen real estate and opt for a 13-inch notebook. The MacBook Pro delivers enough power to work with photos in Adobe Lightroom, and can handle some lighter video editing.
Apple MacBook Pro 13-Inch (2017, Touch Bar) Review
Sony Card Reader
Sony SD/XQD Card Reader
Sadly, Apple ditched the SD card reader from the latest generation of MacBooks. You can debate as to whether or not this was a bad decision (it was), but the end result is that I need to carry a card reader when traveling. This Sony model supports SD and XQD with transfers at USB 3.0 speeds.
$699.99 at T-Mobile
I finally upgraded my phone this year. I had been using an iPhone 6 Plus for the past three, and its battery life had gotten so bad that I had to use a battery case and carry a power bank just to get through a day of travel. I'm really enjoying the 8 Plus. It's a lot faster, and the dual cameras are a lot better than what the 6 Plus has. (And if you're wondering about the wallpaper, it's just that I love Tom Selleck. And I've got to stay on brand.)
Apple iPhone 8 Plus Review
B&W C5 Headphones
Bowers & Wilkins C5 Series 2
I've still got wired headphones, so I'm living the dongle life. I can jam out to John Prine and Tom T. Hall during my commute, enjoying the solid audio quality delivered by the B&W C5 Series 2 earbuds. I've replaced the standard tips with memory foam for a better fit. And, because they're wired, I can also use them to monitor audio when recording video on the a7R III.
Bowers & Wilkins C5 Series 2 Review
Lumu Power
This little dome, the Lumu Power, is an add-on light meter for my iPhone. It's small, so I can keep it in my bag, and comes in handy. I typically just rely on the in-camera meter, but when working with strobes in the studio or in the field I can use its flash meter function to nail exposure settings without any guesswork.
Lumu Power Review
The Best Canon EF-M Mirrorless Lenses for 2022
The Best Sony Mirrorless Lenses for 2022
The Best Full-Frame Cameras for 2022


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