As we gear up for 2019, we are very excited to announce the latest release of Redis Enterprise which marks a significant milestone in our journey towards a zero latency future, and comes packed with all sorts of goodies. Let's review three capabilities that make the new Redis Enterprise especially interesting.
RedisGraph is a Redis module that represents connected data as adjacency matrices instead of the more common adjacency lists per data point representation. By using sparse matrices and employing the power of GraphBLAS (a highly optimized library for sparse matrix operations), RedisGraph delivers a fast and efficient way to store, manage and process graphs — we're talking up to 600 times faster than other graph databases. RedisGraph is now part of a brand new Redis Enterprise module available for our VPC and software customers, and can also be used under our source available license. You can read about the benchmarks on our blog here and get more details about RedisGraph here.
Streams is a new data structure that was introduced with open source Redis 5.0 and is now available in the latest version of Redis Enterprise. Similar to the Lists data type, Streams has an ordered collection of elements called messages. Unlike Lists, however, messages are added exclusively to the end of Streams. In Streams, messages are stored using unique sub-second timestamp-based identifiers, and the order of the messages is immutable. With blocking read functionality, Stream provides a pub/sub like functionality but with fan out scaling ability. Streams has many interesting real-world uses like log aggregation, real-time sentiment analysis and more. We cannot wait to see how the community will put it to use to process data generated at incredible velocities. You can read more about Streams here.
As part of the current Redis Enterprise release, we are also incredibly proud to collaborate with the creators of the two most popular Redis clients — Jonathan Leibiusky, the creator of Jedis, and Andy McCurdy, the creator of Redis-py. We will continue to contribute to these projects as part of our commitment to the Redis community. We plan to ensure that all new features released as part of Redis will be supported in these clients, including Streams and modules. We believe it is important to make sure that these highly popular libraries will be constantly maintained and up to date with the latest capabilities of Redis.


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\section{Introduction}
Experimental realization of quantum computers is closely linked to the theoretical developments in describing interactions between distant qubits mediated by waveguides \cite{kimble2008quantum}. Aiming to uncover the physics behind such interactions, waveguide quantum electrodynamics (QED) has the potential to aid with the development of quantum technologies in many fronts including but not limited to quantum memory, communication, sensing and routing \cite{corzo2019waveguide,calajo2019exciting,goban2015superradiance,degen2017quantum,lvovsky2009optical,shomroni2014all,sipahigil2016integrated}. On the other hand, the theoretical advancements in waveguide QED are limited by our ability to describe macroscopically separated systems, where time-delayed non-Markovian feedback effects dominate and render many simplifying assumptions irrelevant \cite{grimsmo2015time,nemet2019comparison,guimond2017delayed,pichler2016photonic}.

Theoretical waveguide QED community has developed a multitude of methods to tackle the modeling issues associated with waveguide mediated interactions between qubits. Some examples are real-space approaches for few-photons, input-output formalism for describing asymptotic and steady-states, generalized master equations particularly well-suited for describing many-photons and the SLH formalism with its simple set of rules \cite{zheng2010waveguide,shen2007strongly,bermel2006single,cheng2016single,shen2018exact,dinc2019exact,roulet2016solving,roulet2016solving,caneva2015quantum,rephaeli2013dissipation,rephaeli2013dissipation,fan2010input,shi2015multiphoton,baragiola2012n,shi2009lehmann,shi2011two,combes2018two,brod2016two,gonzalez2013non}. Among those methods, many had been employed to describe interactions between distant qubits; yet, while some perform numerical or semi-analytical calculations \cite{fang2018non,liao2015single,calajo2019exciting,dinc2019exact,lalumiere2013input,chen2011coherent,sato2012strong,albrecht2019subradiant,liao2016dynamical} others perform simplifying assumptions such as N-pole approximation or superradiance condition assumption \cite{sinha2020non,zheng2013persistent}. However, a method for describing exact and fully analytical non-Markovian time-evolution is missing from the literature.

The challenge of performing analytical time-evolution of a given Hamiltonian is not a new concept in the quantum physics literature. Even for introductory examples in quantum mechanics and quantum optics \cite{griffiths2010introduction,grynberg2010introduction}, many elementary problems are solved numerically or with simplifying assumptions. Similarly in \cite{dinc2019exact}, we have shown that the analytical non-Markovian time-evolution in single-photon waveguide QED is one analytically-hard-to-compute integral away from our reach, but available semi-analytically. Like every other difficult problem, we need to shift our perspective and tackle the problem with a solid intuition and a clear motivation. The intuition comes from the locality of interactions between qubits due to point-coupling \cite{trivedi2019point}, whereas the motivation stems from a nearly century-old causality question arisen from Fermi's 1932 paper \cite{fermi1932quantum}, which still needs to be answered for multi-qubit waveguide QED.

A cause cannot have an effect propagating faster than the speed of light, a fundamental principle widely referred to as the \emph{causality}. This principle is at the heart of all quantum field theories, effective or otherwise, yet has been shown to be violated by two central concepts of the quantum electrodynamics (QED) literature: i) the rotating-wave approximation (RWA) performed at the Hamiltonian level  \cite{hegerfeldt1994causality,Compagno_1989,funai2019faster}. ii) the concept of a photon wave function in real-space \cite{sipe1995photon}. On the other hand, causality has emerged \emph{exactly} \cite{fang2018non,xu2015input,dinc2019exact} and approximately \cite{sanchez2018emergent} many times in waveguide QED.

Despite utilizing a wave-function approach, real-space formalism has not predicted any non-causal spontaneous emission dynamics so far. Similarly, RWA-related non-causality had been cured by another approximation performed by Fermi in his 1932 paper \cite{fermi1932quantum} -- namely the extension of integral bounds to negative energies. Ever since, Fermi's two atom problem has been used as a benchmark to check whether causality in a theory is violated. In 1995, \cite{milonni1995photodetection} has shown that the negative frequency approximation deletes the non-causal terms, which would have been cancelled by the contributions coming from the non-rotating terms. Consequently, many studies in waveguide QED use the negative frequency extension \cite{zheng2013persistent,tsoi2008quantum}. In fact, a recent study shows that the negative-frequency extension leads to the exact and analytical result for the spontaneous emission from an initially excited qubit and is therefore an essential part of the formalism \cite{dinc2019exact}. Another recent study has studied Fermi's two atom problem in circuit QED using Heisenberg picture \cite{sabin2011fermi}, showing that causality is not violated in this setup. However, a rock-solid argument of causality for multi-qubit systems can be made only with analytical time-evolution of general multi-qubit systems.

In this paper, we develop a diagrammatic approach that gives \emph{exact and fully analytical non-Markovian time evolution} in single-photon waveguide QED. We find the detuned (absolute) momentum space diagram rules that can be used to calculate time evolution without explicit computation. By revisiting Fermi's two atom problem equivalent in waveguide QED, we show that non-Markovian waveguide QED is safe from the non-causal behavior discussed in the literature regarding both RWA and photon wave-function. Finally, using causality arguments, we introduce and prove the no upper half-plane poles (no-UHP) theorem, a waveguide QED analogy to previously known causality theorems in quantum theory \cite{gellmann1954use,schutzer1951onthe}. No-UHP theorem can be used to probe whether results of any calculation in waveguide QED respects the causality principle, hence provides a sanity check for future research.

The main contributions of this paper are to introduce and develop the diagrammatic method, discuss causality in waveguide QED, and prove no-UHP theorem. While other diagrammatic approaches exist in waveguide QED, our method is distinct from them. These diagrams help finding the steady-state solution (S-matrix elements) \cite{see2017diagrammatic,pletyukhov2012scattering}, consider a single-qubit utilizing operational translation of the atomic nonlinear response \cite{roulet2016solving} or provide perturbative solutions in the Heisenberg picture \cite{sabin2011fermi}, our diagrams find exact time-evolution for many-qubit systems utilizing locality principle. To the best of our knowledge, this is the first work considering fully analytical time dynamics of multiple emitters in non-Markovian regime and exact solution of the time-dependent Schr\"odinger equation without any further approximation or assumption.

For the entirety of this work, we encounter two sources of non-Markovianity: i) due to the finite width of single-photon wave-packets \cite{valente2016non,fang2018non} ii) due to finite propagation time between qubits \cite{dinc2019exact,zheng2013persistent,sinha2020non,dinc2019non}. Thus, our consideration of non-Markovianity is uniquely determined by the Schr\"odinger time evolution, system geometry and the initial conditions. As our interests lie in introducing the diagrammatic method for time-evolution and answering the causality question for multi-qubit systems, we do not consider non-radiative decay or any additional noise added to the system, which are natural extensions of the results presented in this paper.

\section{Theory of Diagrams}
In this section, we develop our diagrammatic method starting from the Hamiltonian and the equations of motion. We first show that the equations of motion for the field amplitudes and qubit excitation coefficients (together, we simply call them \emph{amplitudes}) are local owing to the point-coupling nature of interactions. Later, we use the locality principle to divide the scattering processes into unit cells, where a specific \emph{event}, a physical process described by a diagram, can be described by cascading multiple unit cells. We associate a set of rules with each unit cell, which performs the computation of complex integrals automatically. Finally, we use the diagram rules to perform an example amplitude computation for an example diagram and provide a systematic method for finding all diagrams that contribute to the calculation of a specific amplitude.

\subsection{Hamiltonian and equations of motion}
We motivate our approach for a linear chain of $N$ equally-separated (with a distance $L$) identical qubits coupled to a one-dimensional waveguide, although neither assumptions are necessary. The Hamiltonian for such a system can be given as $H = H_0 + H_I$, where
\begin{equation}
    \begin{split}
    H_{0}={}& \Omega \sum_{Q\in\{\rm qubits\}} \sigma_Q^\dag \sigma_Q + i \hbar v_g \int_{-\infty}^\infty \diff x\\
    & \times\left( C_L^\dag(x)\frac{\partial}{\partial x} C_L(x) -C_R^\dag(x)\frac{\partial}{\partial x} C_R(x)  \right)
    \end{split}
\end{equation}
is the free Hamiltonian. $\sigma_Q^\dag$ is the excitation operator for the qubit $Q$, $v_g$ is the group velocity (for simplicity $v_g=\hbar=1$), $C_{R/L}^\dag(x)$ are creation operators for right/left moving photons. Similarly,
\begin{align}
    \begin{split}
    H_{I}={}&\sqrt{\gamma_0/2} \sum_{Q\in\{\rm qubits\}} \int_{-\infty}^\infty \diff x \delta(x-QL)\\
    &\times\left( (C_R^\dag(x)+C_L^\dag(x)) \sigma_Q + \text{H.c.} \right)\,,
    \end{split}
\end{align}
is the point-coupling interaction Hamiltonian with $\gamma_0=2J_0$ being the single emitter decay rate\footnote{Throughout this paper, we sometimes use $J_0$ over $\gamma_0$ when it is algebraically convenient.}. There are several assumptions of the real space Hamiltonian \cite{dinc2019exact}: The rotating-wave approximation is employed when obtaining $H_I$, we assume that we are interested in energy levels $E_k = \Omega \pm O(\gamma_0)$ with $\gamma_0 \ll \Omega$.

In \cite{dinc2019exact}, we considered the time evolution of single-excitation states by re-constructing the time-evolution operator using the energy-eigenstates. It has lead us to finding exact and analytical time-evolution under the Markovian approximation and semi-analytical time-evolution for non-Markovian systems. In this paper, to find analytical time-evolution for general non-Markovian systems, we consider a general single-excitation state
\begin{equation}\label{eq:gentimeevol}
\begin{split}
        \ket{\psi(t)}&=\int_{-\infty}^\infty \diff x [\psi_L(x,t)C_L^\dag(x)\\ &+\psi_R(x,t)C_R^\dag(x)] \ket{0} + \sum_Q e_Q(t) \ket{e_Q},
\end{split}
\end{equation}
where $\psi_{R/L}(x,t)$ are right/left-moving field amplitudes, $e_Q(t)$ are the qubit excitation coefficients and $\ket{e_Q}=\sigma^\dag_Q \ket{0}$. Here, the most general single-excitation state is a superposition of a photon moving to the right and the qubits are all in the ground state ($\int_{-\infty}^\infty \diff x [\psi_R(x,t)C_R^\dag(x) \ket{0}$), a photon moving to the left and the qubits are all in the ground state ($\int_{-\infty}^\infty \diff x [\psi_L(x,t)C_L^\dag(x) \ket{0}$), the field is in vacuum state and individual qubits are in the excited state ($e_Q(t) \ket{e_Q}$). The photon wave-packet can either be generated from the qubits, or it could also come from the initial conditions as an incident pulse, or can include contributions from both cases.

The time evolution of the state $\ket{\psi(t)}$ follows the Schr\"odinger equation $i\partial_t \ket{\psi(t)}=H \ket{\psi(t)}$. After straightforward algebra (See Appendix \ref{sec:appA}), we find the time evolution equation for $\psi_{R/L}(x,t)$ and $e_Q(t)$ as
\begin{subequations} \label{eq:eom}
\begin{align}
    i (\partial_t-\partial_x) \psi_L(x,t)&=\sqrt{\frac{\gamma_0}{2}}\sum_Q e_Q(t) \delta_Q, \label{eq:eom1} \\
    i(\partial_t+\partial_x)\psi_R(x,t)&=\sqrt{\frac{\gamma_0}{2}}\sum_Q e_Q(t) \delta_Q, \label{eq:eom2} \\
    \forall Q, \, (i\partial_t-\Omega) e_Q(t) &= \sqrt{\frac{\gamma_0}{2}} \psi(x_Q,t) \label{eq:eom3}.
\end{align}
\end{subequations}
Here, we define $\psi(x,t)=\psi_R(x,t)+\psi_L(x,t)$ and $\delta_Q = \delta(x-x_Q)$ as short-hand notations. We emphasize that Eqs. (\ref{eq:gentimeevol}-\ref{eq:eom}) apply to a general case and do not contain any assumptions regarding where the qubits are located, or even how many qubits there are. With slight adjustments (to $\Omega$ and $\gamma_0$), they can also describe non-identical qubits. Using Eq. (\ref{eq:eom}), we re-derive the time-evolution equations for the single qubit \cite{fang2018non} and $N$ qubits \cite{liao2015single} from a real-space perspective in Appendices \ref{sec:app2} and \ref{sec:app3} respectively, where we correct some typos from both papers.

\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{Figure1.pdf}
    \caption{\textbf{a} The time evolution of pulse scattering for a single qubit. The red dashed dotted arrows correspond to incident pulses, whereas solid black arrows correspond to transmitted pulses. \textbf{b} A pulse is generated by an initially excited qubit and travels to an adjacent qubit (top), a pulse is incident from far left on a single qubit (bottom). Regardless of incident pulse's source of origin, the two scenarios are equivalent in terms of the local equations of motion at the second qubit.}
    \label{fig:fig1}
\end{figure}

\subsection{Motivating the diagrams: Locality}

Before mathematically discussing locality, we make three important remarks here:
\begin{enumerate}
    \item For $x\neq x_Q$, the field behaves like a free-field, where the field is simply translated in a shape-preserving way.
    \item The existence of source terms leads to non-continuities at the right/left moving field at the atomic position such that
    \begin{equation}
        \psi_{L/R}(x_{Q^+},t)=\psi_{L/R}(x_{Q^-},t) \pm i\sqrt{J_0} e_Q(t).
    \end{equation}
    This also suggests that while the right/left moving components are discontinuous, the field itself $\psi(x_Q,t)=\psi_L(x_Q,t)+\psi_R(x_Q,t)$ is continuous at the qubit position.
    \item The discontinuity of the right/left moving components at a qubit position depends only on the excitation of the corresponding qubit, that is, the interaction Hamiltonian derives changes in the field \emph{locally}. Similarly, the feedback from the field to the qubit is also local due to Eq. (\ref{eq:eom3}). Hence, for the scattering of a pulse from a qubit, only the shape of the incoming field \emph{at the atomic position} is important and other parameters such as the qubit number are irrelevant. The source of the incoming pulse is irrelevant, as a geometry with only a single qubit would lead to the same local EoM as the one with many qubits, which we shortly discuss.
\end{enumerate}

To illustrate the emergence of locality in equations of motion, we first make the piece-wise substitution:
\begin{subequations} \label{eq:localeqs}
\begin{align}
    \psi_R(x,t)&=\sum_Q f_Q^{(R)}([x-x_Q]-t) \\
    &\times [\Theta(x-x_Q)-\Theta(x-x_{Q+1})], \nonumber \\
    \psi_L(x,t)&=\sum_Q f_Q^{(L)}([x-x_Q]+t) \\
    &\times[\Theta(x-x_Q)-\Theta(x-x_{Q+1})]. \nonumber
\end{align}
\end{subequations}
Here, $\Theta(x)$ is the Heaviside function. To cover the boundaries, one could assume that $x_{0}=-\infty$ and $x_{N+1}=\infty$. Otherwise, $x_{Q+1}=x_Q+L$. Setting these equations into Eq. (\ref{eq:eom}), we obtain
\begin{subequations} \label{eq:localeqs2}
\begin{align}
    f_Q^{(R)}(-t)-f_{Q-1}^{(R)}(L-t) &= - i \sqrt{\frac{\gamma_0}{2}} e_Q(t), \\
    f_Q^{(L)}(t)-f_{Q-1}^{(L)}(t+L) &= i \sqrt{\frac{\gamma_0}{2}} e_Q(t), \\
    (i\partial_t - \Omega)e_Q(t) &= \sqrt{\frac{\gamma_0}{2}} [f_Q^{(R)}(-t)+ f_Q^{(L)}(t)].
\end{align}
\end{subequations}
These are indeed local equations, which only depend on the qubit $Q$ and the incoming and out-going fields. In these equations, we can consider the incoming fields ($f_{Q-1}^{(R)}([x-x_{Q-1}]-t)$ and $f_Q^{(L)}([x-x_Q]+t)$) as incident pulses to the qubit $Q$, after which $e_Q(t)$ as well as $f_Q^{(R)}([x-x_Q]-t)$ and $f_{Q-1}^{(L)}([x-x_{Q-1}]+t)$ can be uniquely determined. We illustrate this for a single qubit in Fig. \ref{fig:fig1}a.

In other words, we can consider the time evolution of the field-qubit system as a local phenomenon, where we consider the incoming fields as initial conditions. Of course, $f_{Q-1}^{(R)}([x-x_{Q-1}]-t)$ and $f_Q^{(L)}([x-x_Q]+t)$ do not always come from initial conditions, rather they result from the scattering of light from adjacent qubits, e.g. they are out-going pulses for some other qubit $Q'$. On the other hand, the equations of motion do not distinguish between the two cases. The field and the qubit excitation coefficients update locally, the source of the incoming field does not matter. We illustrate this in Fig. \ref{fig:fig1}b, where the two scenarios are mathematically equivalent.

In the end, we will have developed a recursive method that starts from the initial conditions and updates the field and excitation coefficients one by one at qubit positions, by taking the output of one qubit as the input of the next. We will summarize the complicated calculations in this method in terms of simple diagrams and the corresponding set of rules. But first, we need to take a step back and recall the time evolution for a single qubit, which will be required when constructing the diagram rules.

\subsection{Single qubit time evolution}
We have considered the time evolution for a single qubit analytically in \cite{dinc2019exact}, which we summarize in this section. Let us consider a qubit situated at the position $x=0$. The time evolution of any single-excitation state can be given by \cite{dinc2019exact}
\begin{equation}
\begin{split}
        \ket{\psi(t)}= & \,{} U(t)\ket{\psi(0)}, \quad \text{where} \\
        &U(t)=\frac{1}{2\pi} \int_{-\infty}^\infty \diff k \ket{E_k}\bra{E_k} e^{-iE_kt}.
\end{split}
\end{equation}
The energy eigenstates (with energy $E_k=|k|$ and momentum $k$, for $k>0$) for this system, which describe the scattering of plane-waves from the qubit \cite{shen2005coherent}, can be given as
\begin{equation}
\begin{split}
        \ket{E_k}&=\int \diff x [e^{ikx}\Theta(-x)+t_ke^{ikx} \Theta(x)]C_R^\dag(x) \ket{0} \\
        &+ \int \diff x r_ke^{-ikx}\Theta(-x) C_L^\dag(x) \ket 0 + e_k \sigma^\dag \ket{0}.
\end{split}
\end{equation}
For $k<0$, we simply take the projection of $\ket{E_k}$ w.r.t. the origin \cite{dinc2019exact}. Here, $t_k$,$r_k$ and $e_k$ are:
\begin{subequations}
\begin{align}
    t_k &= \frac{\Delta_k}{\Delta_k+iJ_0},\\
    r_k&= \frac{-iJ_0}{\Delta_k+iJ_0},\\
    e_k&= \frac{\sqrt{J_0}}{\Delta_k+iJ_0},
\end{align}
\end{subequations}
where $\Delta_k=E_k-\Omega$ is the detuning energy. Then, the time evolution of an arbitrary state $\ket{\psi(t)}$ can be given as
\begin{equation}
    \ket{\psi(t)} = \frac{1}{2\pi} \int \diff k \braket{E_k}{\psi(t=0)}\ket{E_k} e^{-iE_k t}.
\end{equation}
This time-evolution equation will be employed in Appendix \ref{sec:app4} when deriving the diagram rules which we introduce shortly.

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{Figure2.pdf}
    \caption{A heuristic illustration of diagrams. \textbf{a} There are three physical components of the diagrams: qubits and right/left-moving photons. \textbf{b} An example event whose amplitude can be calculated using the diagrams. A photon is emitted by the qubit A, propagates for some distance and gets re-absorbed by the qubit B. \textbf{c} The illustration of the event in terms of diagrams. The diagrams break down the complete event into smaller unit cells, for each cell there is a special rule to calculate the input-output relation. Each unit cell is governed by the local equations of motion, whereas cascading defines the initial conditions for the next unit cell such that the output of one unit cell is the input of another. Diagrams are convenient ways of solving Schr\"odinger equation for the single-photon subspace without any explicit computation.}
    \label{fig:fig2}
\end{figure*}

\subsection{An intuitive introduction to diagrams}
So far, we have set up the local equations of motions, established a local equivalence between multi-qubit systems and a single qubit and recalled the real-space method discussed in \cite{dinc2019exact} that allows finding the fully analytical time-evolved state for a single qubit. Our main goal is to bring these concepts together in a simple way such that we can calculate the analytical time evolution of any state in single-photon waveguide QED with multiple emitters. The missing link is provided by the diagrams that we introduce in this section, which dissect a multi-qubit system into smaller pieces that contain at most a single qubit. Since we know the time-evolution of single qubits from the previous section and Appendix \ref{sec:app4}, we can find the time-evolution of these smaller pieces and hence of the whole diagram.

We start with some simple definitions. Events are physical processes that happen in super-positions of each other, whereas diagrams, by definition, are illustrative descriptions of events that help calculating physical amplitudes. In Fig. \ref{fig:fig2}, we describe an example event including two qubits. Fig. \ref{fig:fig2}a shows the physical components of the event, which are qubits and photons. The qubits are represented with orange colored circles, whereas photons are represented with arrows. In Fig. \ref{fig:fig2}b, we describe a specific physical event where qubit A emits a photon, which is later absorbed by a second qubit B. This event is in super-position with many others that describe the spontaneous emission in the case of two qubits. We pick this one specifically, as it is the simplest event possible, hence corresponds to the most elementary diagram. Fig. \ref{fig:fig2}c shows the corresponding diagram, which contributes to the calculation of the excitation coefficient for the qubit B.

The diagrams consist of three or more unit cells, where a unit cell is the smallest portion of the diagram that includes at most a single-qubit and for which an input-output rule exists. There are three types of unit cells: i) starters ii) propagators iii) finishers. In Fig. \ref{fig:fig2}c, there are one of each. The emission of the photon by the qubit A is a starter, propagation without interaction is a propagator, and the absorption of the photon by the qubit B is a finisher. In an arbitrary diagram, there is one starter and finisher each, but there is no limit on the number of propagators.

Before discussing the specific rules, we emphasize two important discussion points:
\begin{enumerate}
    \item Our diagrams are not Feynman diagrams, we do not consider asymptotic or steady-states, we consider the exact time evolution of an initial state. The asymptotic solutions for waveguide QED can be found using the input-output approach or many others, which have already been discussed in the literature \cite{fan2010input}. The input-output relations described by diagrams in this work are not related to this type of input-output formalism at all.
    \item The diagrams solve the time-dependent Schr\"odinger equation, whose solution is unique once the initial and boundary conditions are well-defined. Thus, the diagrams uniquely determine the exact solution.
\end{enumerate}

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{Figure3.pdf}
    \caption{A visual summary for the set of diagrammatic rules. If followed, they provide exact and analytical non-Markovian time evolution for single-photon waveguide QED.}
    \label{fig:fig3}
\end{figure*}

\subsection{The set of diagrammatic rules}
In this section, we introduce the diagrammatic rules post-hoc and derive them from starting principles in Appendix \ref{sec:app4}. There is a total of four basic rules:

\begin{rules}[The unit cell compartmentalisation]
For each diagram associated with are the detuned (absolute) momentum space ($\Delta_k$) representation of states and a time component ($\tau$) that keeps track of propagation delay of photons due to finite speed of light. The diagrams are divided into smaller unit cells that keep track of both quantities. There are three types of unit cells: starters, propagators and finishers.

Momentum space component: All unit cells except for starters have an input, $f_{\rm in}(\Delta_k)$, and all except for finishers have an output, $f_{\rm out}(\Delta_k)$. Starters are associated with a unique $f_{\rm out}(\Delta_k)$, propagators have an input-output relationship between $f_{\rm in}(\Delta_k)$ and $f_{\rm out}(\Delta_k)$, finishers are associated with a unique amplitude calculation rule that determines the excitation coefficients ($e_Q(t)$) or the field-amplitudes ($\psi_{R/L}(x,t)$) utilizing $f_{\rm in}(\Delta_k)$.

In the case of cascaded unit cells, the output of the previous cell is the input of the next:
\begin{equation}
     f_{\rm in}^{(i+1)}(\Delta_k) = f_{\rm out}^{(i)}(\Delta_k).
\end{equation}
Time component: Some propagators update the time component ($\tau$) by introducing a time-delay, the time-delay is propagated within the cascades.
\end{rules}

\begin{rules}[Starters]
There are two possible starter unit cells: i) an initially excited qubit ii) an initial pulse. The output of the starter unit cells can be given
\begin{enumerate}
    \item For an initially excited qubit:
    \begin{equation}
        f_{\rm out} (\Delta_k)=\frac{\sqrt{J_0}}{(\Delta_k+iJ_0)}.
    \end{equation}
    \item For an initial pulse with $\psi_{R/L}(x,t=0)=f(x)e^{\pm i \Omega x}$:
    \begin{equation}
        f_{\rm out}(\Delta_k)=\int_{-\infty}^\infty \diff x f(x) e^{\mp i \Delta_k x}.
    \end{equation}
\end{enumerate}
For both starters, the time component starts as $\tau=t$.
\end{rules}

\begin{rules}[Propagators]
There are three types of propagators: i) propagation without interaction ii) transmission through a qubit iii) reflection from a qubit. The input-output relationships for the propagator unit cells can be given
\begin{itemize}
    \item For propagation without interaction for a distance $L$:
    \begin{equation}
        f_{\rm out}(\Delta_k) = f_{\rm in}(\Delta_k), \quad \tau_{\rm out} = \tau_{\rm in}-L.
    \end{equation}
    \item For transmission through a qubit:
    \begin{equation}
         f_{\rm out}(\Delta_k) = f_{\rm in}(\Delta_k) t_k, \quad \tau_{\rm out} = \tau_{\rm in}.
    \end{equation}
    \item For reflection from a qubit:
    \begin{equation}
         f_{\rm out}(\Delta_k) = f_{\rm in}(\Delta_k) r_k, \quad \tau_{\rm out} = \tau_{\rm in}.
    \end{equation}
\end{itemize}
\end{rules}

\begin{rules}[Finishers]
There are two types of finishers: i) qubit excitation coefficient ii) right/left-moving field amplitudes. The calculation of observables for the finishers can be given
\begin{enumerate}
    \item For qubit excitation coefficients
    \begin{equation}
        e_Q(t) = \frac{e^{-i\Omega \tau_{\rm in}}}{2\pi} \int_{-\infty}^\infty \diff \Delta_k f_{\rm in}(\Delta_k) e_k e^{-i\Delta_k \tau_{\rm in}}.
    \end{equation}
    \item For right/left-moving field amplitudes
    \begin{equation}
        f^{(R/L)}_Q(x,t)=\frac{e^{-i\Omega \tau_{\rm f} }}{2\pi} \int_{-\infty}^\infty \diff \Delta_k f_{\rm in}(\Delta_k) e^{-i\Delta_k \tau_{\rm f}},
    \end{equation}
    where $\tau_{\rm f}=\tau_{\rm in} \mp (x-x_0)$ for right/left-moving field amplitudes with $x_0$ being the position of the final qubit that the photon has scattered from.
\end{enumerate}
\end{rules}

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{Figure4.pdf}
    \caption{Systematic approach for finding the event diagrams that contribute to the amplitude calculations. For illustration purposes, we consider $N=3$ qubits with the initial condition that the middle qubit is excited. The qubits are separated by $L$. To find the event diagrams, we start with a fractal tree and branch out at every scattering point. If the photon leaves the system, the branch is terminated, as is the case for the two out of four branches at the final step. Earlier branches describe earlier times, which are noted with horizontal dotted red lines. The event diagrams are illustrated on top of the branch arrows.}
    \label{fig:fig4}
\end{figure*}

We visually summarize the diagram rules in Fig.~\ref{fig:fig3}. The diagrams give the qubit excitations $e_Q(t)$ and local field amplitudes $f_Q^{(R/L)}$, from which we can find $\psi_{R/L}(x,t)$ via Eq. (\ref{eq:localeqs}).

\subsection{An example diagram calculation for the event in Fig. \ref{fig:fig2}b}
Using the diagrammatic rules, let us calculate the excitation coefficient for the qubit $B$ for the event given in Fig. \ref{fig:fig2}b, with the initial condition that the qubit $A$ is initially excited. We will perform the calculations step by step for illustration purposes.

As we mentioned before, there are three unit cells in this example. Let us start with the starter:
\begin{equation}
    f_{\rm out}^{(1)}(\Delta_k)= \frac{\sqrt{J_0}}{\Delta_k+iJ_0}, \quad \tau=t.
\end{equation}
Now, by the cascading rule, we know that $f_{\rm in}^{(2)}(\Delta_k)=f_{\rm out}^{(1)}(\Delta_k)$ and by the propagator rule
\begin{equation}
    f_{\rm out}^{(2)}(\Delta_k)=f_{\rm in}^{(2)}(\Delta_k)=\frac{\sqrt{J_0}}{\Delta_k+iJ_0}, \quad \tau=t-L.
\end{equation}
Once again, by the cascading rule,  $f_{\rm in}^{(3)}(\Delta_k)=f_{\rm out}^{(2)}(\Delta_k)$. Finally, using the finisher rule, we obtain
\begin{equation}
\begin{split}
        e_B(t)&= \frac{e^{-i\Omega (t-L)}}{2 \pi} \int_{-\infty}^\infty \diff \Delta_k f_{\rm in}^{(3)}(\Delta_k) e_k e^{-i\Delta_k (t-L)}, \\
        &= \frac{e^{-i\Omega (t-L)}}{2 \pi} \int_{-\infty}^\infty \diff \Delta_k \frac{J_0}{(\Delta_k+iJ_0)^2} e^{-i\Delta_k (t-L)}, \\
        &= -J_0 (t-L) e^{-(J_0+i\Omega)(t-L)} \Theta(t-L).
\end{split}
\end{equation}
We have calculated the amplitude corresponding to this event. However, this specific event describes this problem only for $t<3L$. For later times, there will be other events, hence diagrams, that contribute to this amplitude.
\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{Figure5.pdf}
    \caption{Fermi's two atom problem in waveguide QED \textbf{a} Two identical qubits are coupled to a one-dimensional waveguide. The first qubit is initially excited, the second one is initially in the ground state. The first qubit spontaneously decays with a rate $\gamma_0$, whereas the emitted photon is picked up by the second qubit after some time delay due to photon propagation. \textbf{b} All diagrams contributing to the qubit excitation coefficient $\braket{e_{1}}{\psi(t)}$, where $\ket{\psi(t=0)}=\ket{e_{-1}}$. Using the diagrams, one can answer Fermi's two atom problem for waveguide QED.}
    \label{fig:fig5}
\end{figure*}

\subsection{Fractal trees for finding all events}
In general, for given initial conditions and qubit configuration, there are many events that contribute to the amplitudes. The exact time-evolution for the amplitudes can be found by summing over all possible diagrams/events. This leads to a solution in terms of a time-series expansion, which is exact. Luckily, the more complicated events with multiple propagators start contributing at later times due to the propagation delay introduced within the system. Thus, the early terms in the time-series expansion can be found with simple diagrams. In fact, for a given final time $t_f$, we use a binary fractal tree to find all possible diagrams that contribute to the time-series expansion such that the exact time evolution is obtained for $t<t_f$. This is possible due to the binary nature of scattering (transmission or reflection) of light from a qubit in a one-dimensional waveguide.

We illustrate the binary fractal tree for an example of $N=3$ qubits in Fig. \ref{fig:fig4}. In this specific tree, we keep track of the right/left-moving field amplitudes, whereas the event diagrams for the excitation coefficients can be written down in a similar way. For any given final time of interest $t=t_f$, one needs to keep branching out the tree such that all the events with delays less than $t_f$ are obtained.

Since the fractal tree branches out rapidly, it is not the most ideal way to find all events for a multi-emitter system. The diagrammatic method requires a more efficient event-finding schema to better describe systems with many emitters. This is not our focus in this paper and we leave it as a future research direction to the literature. For the rest of the paper, we turn our focus to illustrating the power of diagrams for the Fermi's two atom problem, which can be exactly and analytically solved, for the first time, in waveguide QED.

\section{Exact causality in single-photon waveguide QED}
So far, we introduced the diagrammatic approach for finding the analytical non-Markovian time evolution of states in the Schr\"odinger picture. Now, we will leverage this to answer the general question, whether exact causality is preserved in single-photon waveguide QED. In this section, we first start with Fermi's two atom problem, then generalize to any waveguide QED system. Finally, we discuss the Markov approximation that leads to short-distance causality violations inside the multi-qubit system and the consequent emergence of collective decay rates.

\subsection{Fermi's two atom problem}
Fermi's two atom problem has been considered in \cite{sabin2011fermi} for circuit QED using Heisenberg picture from a perturbative approach. Here we find the analytical time evolution in the Schr\"odinger picture, which we show to be exact in Appendix \ref{sec:app5}. Our results in this section agree with the findings of \cite{sabin2011fermi}.

To provide the first test of causality, we now focus our attention to the two-qubit system, where one of them (call it qubit $-1$) is initially in the excited state and emits a photon over time. The second one (call it qubit $1$) is in the ground state and can get excited by some finite probability after some time-delay. The test is whether the second qubit can get excited before $t<L$, as this would mean that a photon can travel faster than light and violate causality. For a causal theory, $e_1(t<L)=0$ should hold.

We now consider the configuration shown in Fig. \ref{fig:fig5}a, where the distance between qubits is $L$ and we pick the middle point of the qubits as the center of the $x$-axis. As an initial condition, we assume that the qubit $-1$ is excited $\ket{\psi(t=0)}=\ket{e_{-1}}$. Then, our aim is to find the amplitude
\begin{equation}
    e_1(t) = \braket{e_1}{\psi(t)}.
\end{equation}

The diagrams contributing to this amplitude are illustrated in Fig. \ref{fig:fig5}b, which echo those found from the perturbative expansion of observables in the Heisenberg picture \cite{sabin2011fermi}. The events corresponding to $n$th diagrams include, an emission by qubit $-1$, an absorption by qubit $1$ and $2n$ reflections with $(2n+1)$ free propagation over length $L$. As $n$ increases, we consider events, where the photon is trapped between the qubits for longer times ($(2n+1)L$ to be precise). These are lower probability events as some portion of the excitation escapes in the shape of a radiating field for every event.

Following the rules we introduced earlier and the diagrams in Fig. \ref{fig:fig5}b, we write the excitation coefficient as
\begin{equation}
    e_1(t) = \sum_{n=0}^\infty e_1^{(n)}(t),
\end{equation}
where $e_1^{(n)}(t)$ corresponds to the $n$th diagram. Then, following the diagram rules, we find
\begin{equation}
\begin{split}
    e_1^{(n)}(t) &= \frac{e^{-i\Omega \tau_n}}{2\pi} \int_{-\infty}^\infty \diff \Delta_k \frac{r_k^{2n} e_k\sqrt{J_0}}{\Delta_k +i J_0}  e^{-i\Delta_k \tau_n}, \\
    &=- \frac{(\tau_n J_0)^{2n+1}}{(2n+1)!} e^{-(J_0+i\Omega)\tau_n}\Theta(\tau_n),
\end{split}
\end{equation}
where $\tau_n = t-(2n+1)L$. Here, we performed contour integration for two cases $t > \tau_n$ and $t< \tau_n$. Bringing all together, we find
\begin{equation} \label{eq:firstqubitexcitation}
    e_1(t) = - \sum_{n=0}^\infty \frac{(\tau_n J_0)^{2n+1}}{(2n+1)!} e^{-(J_0+i\Omega)\tau_n}\Theta(\tau_n).
\end{equation}
We discuss the complete time-evolved state $\ket{\psi(t)}$ in Appendix \ref{sec:app5}, where we show that $\ket{\psi(t)}$ is indeed an exact solution of the Schr\"odinger equation, hence $e_1(t)$ found here is exact. Considering the times $t<L$, we find
\begin{equation}
    e_1(t) = 0, \quad t\leq L
\end{equation}
such that the causality is not violated for the two atom problem. Waveguide QED passes its first test.

\subsection{Generalization of causality: no-UHP theorem}
The second test of waveguide QED is a general one. What if there were more than one waveguide and arbitrary numbers of quantum emitters? Luckily, to prove causality for a general system, we do not need to introduce any more diagrams than we already have discussed.

Consider the first diagram in Fig. \ref{fig:fig5}b, which is the earliest contribution to the excitation coefficient. Indeed, this diagram corresponds to the event we described in Fig. \ref{fig:fig2}. As we discussed then, this diagram (or an equivalent one) is the most elementary diagram which can be built. For any excitation problem, this diagram sets the lower bound on the time it takes to excite a distant qubit. Hence, regardless of the number of qubits or waveguides, the distant qubit cannot be excited before the propagation time has passed. This ensures us that for an initial condition of type 1 (when a qubit is initially excited), single-photon waveguide QED is causal.

When it comes to initial condition type 2, we do not even need the diagrams. From Schr\"odinger equation, it is clear that $H_I \ket{\psi(t)}=0$ unless the field at qubit positions is nonzero. The free Hamiltonian propagates the field with a constant speed of light, which is taken as $v_g=1$ and modulates the phase of the excitation coefficient but cannot change excitation probability. In other words, a qubit in the ground state can only be excited if the field amplitude at the qubit position is non-zero. Thus, the initial condition type 2 does not violate causality either.

Now that we have shown that there are no causality violations in single-photon waveguide QED, we can now motivate the no-UHP theorem. Once again, we start discussing a linear chain of $N$ qubits. Later, we will argue how the results are more general than this specific case.

Consider a linear chain of $N$ qubits, where qubits are located at $x=mL$ with $m=0,\ldots, N-1$. As an initial condition, we pick the state with an incoming decaying exponential
\begin{equation}
    \ket{\psi(t=0)}= \int_{-\infty}^{-x_0} \diff x \sqrt{2\sigma} e^{\sigma (x+x_0)} e^{i\Omega x} C_R^\dag(x) \ket{0},
\end{equation}
where $\sigma \sim O(\gamma_0)$ and $x_0>0$. Then, the time evolution of this state is proportional to \cite{dinc2019exact}
\begin{equation}
    \ket{\psi(t)}\sim \int_{-\infty}^\infty \diff \Delta_k \frac{e^{-i\Delta_k (t-x_0)}}{\Delta_k + i \sigma} \ket{E_{k^+}}.
\end{equation}
Here, we will not keep track of the proportionality factors, as they are not important for our consideration. Moreover, $\ket{E_{k^+}}$ ($k^+$ means that $k>0$) includes the scattering coefficients $e_k^{(m)}$, $r_k$ and $t_k$, as well as occasional $e^{\pm ikx}$ terms. Now, let us compute the excitation coefficient for the qubit $m$ at time $t$
\begin{equation} \label{eq:final}
    \braket{e_m}{\psi(t)} \sim \int_{-\infty}^\infty \diff \Delta_k \frac{e^{-i\Delta_k (t-x_0)}}{\Delta_k + i \sigma} e_k^{(m)}.
\end{equation}
As $x_0 \to \infty$, the field is far away from the qubits. The field amplitude at any qubit position is zero, hence $\braket{e_m}{\psi(t)}=0$. On the other hand, as $x_0 \to \infty$, the contour of the integral in Eq. (\ref{eq:final}) is connected through the upper half-plane. For the integral to be zero, regardless of the time $t$, the coefficient $e_k^{(m)}$ should not have any upper half-plane poles. Similar arguments can be made for $t_k$ and $r_k$ if we consider the field amplitudes instead of the excitation coefficients.

For a more general system with many waveguides, the same argument can be made by picking one waveguide and an initial pulse such as the decaying exponential as in Eq. (\ref{eq:final}). The reason behind choosing the decaying exponential is the following: The decaying exponential is zero for $x>-x_0$, hence cannot excite qubits until later times $t>x_0$. Its momentum representation has only one lower half-plane pole at $\Delta_k = - i \sigma$ and no upper-half plane poles. Then, following the discussion in \cite{dinc2019exact} regarding a general waveguide QED system, integral given in Eq. (\ref{eq:final}) describes the amplitudes with the only exception that $e_k^{(m)}$ is replaced with the corresponding scattering parameter, generalizing our findings regarding causality in linear chains.

Now, we are ready to state the no-UHP theorem:
\begin{theorem}[No-UHP Theorem]
For any waveguide QED system with multiple emitters and waveguides, the scattering parameters do not have any upper half-plane poles.
\end{theorem}
Thus, for any scattering matrix calculation, we expect the resulting matrix elements to have poles only on the lower half-plane or on the real axis. This is a waveguide QED analogy to previously known causality theorems in quantum theory \cite{gellmann1954use,schutzer1951onthe}.

\subsection{Time-delayed coherent quantum feedback, short-distance causality violations and emergent collective decay rates}
\begin{figure}
    \centering
    \includegraphics[width=\columnwidth]{Figure6.pdf}
    \caption{The time-delayed feedback leads to the periodic re-excitation of the second qubit with time intervals of $2L$. \textbf{a} The field mediates the interaction between the two qubits with some time delay. Here, only the field ongoing from qubit 1 to the qubit 2 is shown, where the pale blue corresponds to the future state of the trapped photonic field moving to the right. The feedback waves arise from the internal reflections of the photon. The field amplitudes are illustrated using analytical expressions calculated in Appendix \ref{sec:app5}. \textbf{b} The second qubit gets excited periodically due to the incoming feedback waves for a large separation of $L=5J_0^{-1}$. \textbf{c} The qubits are moderately separated with $L=2J_0^{-1}$, where interference between different feedback waves can be observed. \textbf{d} The qubits are closely separated with $L=0.3J_0^{-1}$ such that from the interference between nearly-instantaneous feedback waves emerges a collective behavior. For all plots, we pick $\Omega = 200 J_0$.}
    \label{fig:fig6}
\end{figure}

Having discussed causality for single-photon waveguide QED, we now turn our attention to a commonly used Markov approximation, where short-distance causality violations are allowed for algebraic convenience when solving the time-evolution of the model. Within this approximation, the time-evolution of single-photon states can be found fully analytically \cite{dinc2019exact}, making it a powerful tool for considering microscopically separated qubits where the quantum coherent feedback mediated by the field is nearly-instantaneous. In this section, we first visualize the feedback for largely separated, even isolated, qubits. Then, using the analytical expressions from Appendix \ref{sec:app5}, we show the emergence of collective decay rates for the two-qubit system in the Markovian limit $L \to 0$ (or more practically, $L \to O(\Omega^{-1})$ with $J_0 \ll \Omega$). In this limit, we ignore any causality violations within $O(\Omega^{-1})$, as any events with such short time duration are assumed to happen instantaneously.

Now, let us consider the interactions in waveguide QED systems from a qualitative point of view. An excited qubit decays to the waveguide, which takes the form of the field excitation. The field propagates with a finite speed $v_g$ (which is taken $v_g=1$ for convenience) and scatters inside the multi-qubit system. A portion of the excitation travels back to the initial qubit with a certain time-delay introduced by the finite propagation speed, re-excites the qubit and the feedback process goes on infinitely many times. We call the portion of the field that re-excites the initial qubit \emph{the feedback waves} (See Fig. \ref{fig:fig6}a). In many cases, the feedback waves get dampened over time such that less and less excitation remains inside the system and more gets radiated away.\footnote{In a very special case, the dampening does not happen, and a finite amount of excitation gets trapped inside the system signaling the existence of so-called \emph{bound-states in continuum} for the specific waveguide QED system \cite{calajo2019exciting}} In this highly qualitative picture, the field trapped between qubits mediates the interactions in a time-delayed manner; and has a memory built-into it through all the scattering inside the system and through the finite, non-zero width of the photon wave-packet. This is, partially, the reason why we primarily keep track of the field scattering in the event diagrams (both in Figures \ref{fig:fig4} and \ref{fig:fig5}) even when we are calculating the qubit excitation coefficients.

Depending on how early or late the consecutive feedback waves arrive back to the initial qubit, the qubits can show a various range of collective behavior. If there is a sufficiently long time (much longer than $J_0^{-1}$) between two feedback waves (See Fig. \ref{fig:fig6}b), the qubits are nearly isolated and not much collective behavior is observed. As the qubit separation decreases (See Figs. \ref{fig:fig6}c-d), the subsequent feedback wave travels back to the original qubit before the decay of the previous wave, leading to time-retarded constructive or destructive interference between multiple consecutive feedback waves. The qubits can no longer be viewed as single isolated entities, but rather they are in waveguide-mediated interactions with each other. These interactions lead to novel collective phenomena such as superradiance, subradiance and bound-states in continuum \cite{dinc2019exact}.

In the limit, where the feedback happens almost instantly, there is almost no field stored between the qubits. This is because $L\sim(\Omega^{-1})$ and $|\psi(x,t)|^2  \sim O(J_0) $ (from diagram rules and Appendix \ref{sec:app5}) such that the probability amplitude of the trapped photon is vanishingly small $\mathcal{P}(x,x+L) \approx L |\psi(x,t)|^2  \sim O(J_0/\Omega) \ll 1$. Thus, the trapped field no longer stores the \emph{memory} of the feedback waves, as they almost instantly arrive. Consequently, we call this limit the \emph{Markovian regime} \cite{dinc2019exact}.

Now, let us re-consider the two-qubit example, specifically Eq. (\ref{eq:firstqubitexcitation}) and show that we can obtain the collective decay rates from this exact expression when we take the Markovian limit. We take the limit $L \to O(\Omega^{-1})$ such that $J_0 L \to 0$, $t \sim O(J_0^{-1})$ and define the phase parameter $\theta = \Omega L$. Then, we obtain for $t>0$
\begin{equation}
\begin{split}
        &e_1(t) =  - \sum_{n=0}^\infty \frac{(\tau_n J_0)^{2n+1}}{(2n+1)!} e^{-(J_0+i\Omega)\tau_n}\Theta(\tau_n), \\
        &\approx  -e^{-(J_0+i\Omega)t} \sum_{n=0}^\infty \frac{(t J_0)^{2n+1}}{(2n+1)!} e^{i\theta(2n+1)} \Theta(t),\\
        &=-e^{-(J_0+i\Omega)t} \sum_{n=0}^\infty \frac{(t J_0e^{i\theta})^{2n+1}}{(2n+1)!}, \\
        &= -\frac{e^{-i\Omega t}}{2} e^{-J_0 t} \sinh(t J_0 e^{i\theta}),\\
        &= \frac{e^{-i\Omega t}}{2} \left( e^{-\frac{\Gamma_1}{2}t} -e^{-\frac{\Gamma_2}{2}t} \right),
\end{split}
\end{equation}
where we read-off the \emph{collective decay rates} as
\begin{subequations}
\begin{align}
    \Gamma_{1/2} = \gamma_0 (1\pm e^{i\theta}).
\end{align}
\end{subequations}
These are indeed the collective decay rates of the two-qubit system \cite{dinc2019exact}. We note, however, in this limit, the second qubit gets excited almost simultaneously after the decay of the first qubit. This leads us to conclude:
\begin{theorem}
Causality is violated for short-distances in the Markovian limit, which can describe the microscopically separated qubits well.
\end{theorem}
Thus, the price of obtaining an analytically convenient and physically intuitive collective picture made available through the Markov approximation is the acceptance of short-distance violations in the system time-evolution.

\section{Conclusion}

Non-Markovian time evolution in waveguide QED is a challenging problem that needs to be tackled in order to aid the theoretical research in waveguide QED. So far, the literature has employed various assumptions and/or numerical approaches to tackle this problem. Among those assumptions, Markovianity has been the most prominent. If qubits are microscopically separated, the propagation time delay between qubits can be neglected (Markovianity assumption). This regime is fairly well-explored in the literature \cite{dinc2019exact} and provides important insights on the collective behavior of the system. If the qubits are separated by large distances, then each qubit behaves in an isolated manner, hence collective effects become unimportant. This regime is easily explorable, as, in this regime, the decay of one qubit happens before another one has the chance to be excited. Interestingly, the mysteries lie at the moderate separation, where both time-delayed feedback and collective interactions dictate the behavior of the system. In fact, interesting phenomena had been observed when multiple qubits are separated moderately, including but not limited to enhanced quantum memory \cite{calajo2019exciting} or enhanced superradiance (or so-called super-superradiance) \cite{dinc2019non,sinha2020non}.

In this work, we have tackled the non-Markovian time evolution problem in single-photon waveguide QED. We have developed a diagrammatic approach, which breaks down the complicated computations into a simple set of rules governing unit cells. With this method, we consider the waveguide QED equivalent of Fermi's two atom problem, show that causality is not violated in single-photon waveguide QED, and  conclude with a discussion on Markov approximation commonly employed in the waveguide QED literature and consequent short-distance causality violations introduced to the time-evolution. In our considerations of causality, we also provide the literature with the no-UHP theorem, which states that S-matrix calculations should not lead to scattering parameters with upper half-plane poles. Both the diagrams and the no-UHP theorem can be beneficial as a sanity check for theoretical research in waveguide QED.

Further research on diagrams is necessary when we consider large systems with many qubits, as the number of possible diagrams increases rapidly following a fractal tree (See, for example, Fig. \ref{fig:fig4}). As future work, a more efficient process is required to find all the diagrams that contribute to the calculations of amplitudes. On the other hand, in such large systems, the early time dynamics can still be exactly captured by the early stages of the fractal tree. Therefore, the diagrams found from the tree can aid the theoretical research in waveguide QED especially in bench-marking theoretical models, as any theory should reproduce the exact results obtained from them. Hence, we provide the literature, for the first time, with the analytical ground truth of the non-Markovian time evolution of single-excitation states driven by the point-coupling Hamiltonian in waveguide QED.

\section*{Acknowledgements}
The author would like to thank the Perimeter Scholars International Essay Defense Committee, Eduardo Martinez, Tibra Ali and Francois David, for insightful questions regarding the causality in real-space formalism; which eventually lead to this work, and Agata Bra\'nczyk and Lauren E. Hayward for supervising the essay.

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Kožlí () is a municipality and village in Písek District in the South Bohemian Region of the Czech Republic. It has about 50 inhabitants.

Etymology
The name of the village was derived either from the personal name Kozel (meaning "Kozel's") or from goat farming (goat = koza in Czech).

Geography
Kožlí is located about  north of Písek and  south of Prague. It lies in the Benešov Uplands. It is situated on the western shore of the Orlík Reservoir, built on the Vltava River. There are also several small ponds, supplied by local brooks.

History

The first written mention of Kožlí is from 1396.

Sights
Northern part of the large park of the Orlík Castle extends into the territory of Kožlí. It includes the Schwarzenberg Tomb, built in the Neo-Gothic style in 1875–1877. It contains the remains of several members of the cadet branch of the House of Schwarzenberg, the most notable being Field Marshal Prince Karl Philipp of Schwarzenberg (1771–1820). The tomb is not open to the public.

References

External links

Villages in Písek District

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Home ThriftBooks The Searcher: A Novel
The Searcher: A Novel
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On Dec 25 2020, a reader said:
"He enjoys this rain. It has no aggression to it; its steady rhythm and the scents it brings in through the windows gentle the house's shabbiness, giving it a homey feel. He's learned to see the landscape changing under it, greens turning richer and wildflowers rising. It feels like an ally, rather than the annoyance it is in the city."
The Searcher is the second stand-alone novel by award-winning Irish author, Tana French. Cal Hooper is settling into his dilapidated house on a piece of land near the tiny village of Ardnakelty in the west of Ireland. He's enjoying the challenge of restoring the place to liveable, and walks in the bracing country air. The locals are more welcoming than he had expected, and he looks forward to fishing, hunting rabbits for stew, and making friends with a treeful of rooks.
He's also enjoying the fact that his "mental alarm systems were switched off, the way he wanted them" but, as he works on mending an old desk out in the yard with his grandfather's tools, "the back of his neck flared. The back of Cal's neck got trained over twenty-five years in the Chicago PD. He takes it seriously" so he waits patiently until the cause, a young teen, gains the confidence to show a face, and even longer, to make a request: worries over the disappearance, six months earlier, of an older brother, plague this younger sibling.
Trey Reddy is convinced that nineteen-year-old Brendan, who would never have left without saying where he was going, has been kidnapped, but the Reddy Family's poor reputation almost guarantees dismissal by the Guard. Cal considers it likely that the young man has run: either to something better than the village can promise; or from some threat, perhaps for something he has done. Could those Dublin drug boys in the pub be involved? Here, though, Cal has no authority, no resources.
Quite contrary his every intention, Cal finds himself making what he believes are subtle enquiries about Brendan Reddy. Of course, in a tiny village like Ardnakelty: "A guy can't pick his nose around here without the whole townland telling him to wash his hands" and he finds himself on the end of an equally subtle warning off. He's made Trey a promise: will he now leave it there? Because "It feels like a vast, implacable failing in his character that he can't come up with just one good solution to offer this scrawny, dauntless kid."
This plays out against a background of hard-drinking local farmers, sheep being mutilated in the night and the youth who don't escape to the city tending towards either mischief or suicide. And in the back of his mind, forty-eight-year-old Cal is still haunted by the failure of his marriage and concerns for the daughter he has somehow apparently let down.
Whatever readers might expect from Tana French, this one is no fast-paced, action-packed thriller; in store is a slow burn read that allows the reader to get to know the protagonist well, to understand this principled ex-cop, his philosophy of life and his observations: "around here mockery is like rain: most of the time it's either present or incipient, and there are at least a dozen variants, ranging from nurturing to savage, and so subtly distinguished that it would take years to get the hang of them all". The support cast, too, is a pleasure to meet: quirky villagers of whom Cal takes their measure to tailor his words and actions to fit. Nonetheless, the plot is intriguing, with red herrings and a twist or two to keep it interesting.
The Irish landscape itself is a character in this novel, and French's descriptive prose is often exquisite: "The next morning is all soft mist, dreamy and innocent, pretending yesterday never happened." With more than one local intent on matchmaking Cal with available women, and a poteen party, there's plenty of dry and sometimes dark humour, not the least in Cal's inner monologue, but also in some of the dialogue: "Face on her like a bulldog licking piss off a nettle." Utterly enthralling.
This unbiased review is from an uncorrected proof copy provided by NetGalley and Penguin UK.
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Anthony Arthur Long is Professor Emeritus of Classics, Irving G. Stone Professor Emeritus of Literature, and Affiliated Professor of Philosophy and Rhetoric at University of California at Berkeley. His recent work has focused on ancient notions of the self. His latest book is Greek Models of Mind and Self(Harvard UP, 2015) and his forthcoming book, with M. Graver, is the translation of Seneca, Letters on Ethics (Chicago UP, 2016). He is also currently working on a new translation with commentary of Plotinus, Ennead II.4, On matter.


Lukas Bieringer (CISPA, l.) talks to Sven Weizenegger (Incubator Advisory Board).
For the first time this year, the "CISPA Incubator Advisory Board" met in Saarbrücken.
After a brief review of activities in 2018, the board discussed upcoming events and challenges of startups at CISPA - Helmholtz Center for Information Security in 2019. The incubator team provided a comprising insight into the operational work as well as ongoing entrepreneurial projects at the center. Moreover, the board members - Sven Weizenegger, Dr. Mathias Bauer, and Philipp von Styp-Rekowsky - got an overview about several future concepts of "CISPA Incubator" and were able to state their opinions about planned approaches.
Furthermore, the meeting provided an opportunity for selected startup teams to pitch their business ideas in front of the well-experienced board members. After a short presentation, every team had to face critical questions from the audience. These mostly covered technological issues and market entry strategies of the arising business models. Although there is no doubt that IT security is a growing future market, the technology-focused teams seized the opportunity to profit from in-depth market insights of the serial entrepreneurs.
In close cooperation with its partners, the "CISPA Incubator" aims at fostering entrepreneurial initiatives within the encompassing spectrum of privacy and cybersecurity as a transversal issue in science, society and economy. Startups and tinkerers are provided with the best preconditions at the melting pot of academia and marketable solutions.
Philipp von Styp-Rekowsky, Founder at Nimiq.


Iran's Foreign Minister Mohamad Javad Zarid said that his country is ready to cooperate with the new Lebanese government, offering support in all sectors.
Speaking to reporters at Beirut's airport upon arriving in Beirut on a two-day visit, Zarif noted that his visit is aimed at showing solidarity with Lebanon and relaying Iran's readiness to provide assistance at all levels.
Zarif said that his country is waiting for Lebanon to show a desire to accept its military assistance, a few days after Hezbollah leader Hassan Nasrallah offered to play a mediation role by asking Iran to supply the Lebanese military with weapons and aerial defense systems to confront Israeli warplanes.
"We always have this type of readiness and we announced on other occasions that this tendency exists in Iran but we are waiting for this desire to exist on the Lebanese side," the Iranian FM said.
Zarif will be holding talks with Lebanon's top officials on Monday, including Prime Minister Saad Hariri, as well as representatives of certain Lebanese parties and Palestinian factions.


Hi, I am interested in your 1976 Porsche 911 (stock #10726) listed on Autotrader for $29,950. I'd like to get more information about this vehicle and confirm its availability.
1976 Porsche 911S Coupe This very presentable 1976 Porsche 911S Coupe is available in its original color code#908 Grand Prix white with a tan interior. It comes equipped with a 2.7 liter with a manual transmission, Fuchs wheels and includes the spare tire, tool kit and jack. A very clean and presentable vehicle which is mechanically sound. For $29,950, This very presentable 1976 Porsche 911S Coupe is available in its original color code#908 Grand Prix white with a tan interior. It comes equipped with a 2.7 liter with a manual transmission, Fuchs wheels and includes the spare tire, tool kit and jack. A very clean and presentable vehicle which is mechanically sound.


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Illuminating experiences: "Mastering Light" exhibition at Vassar
Posted by Frances Marion Platt on April 11, 2022 in Art, Events · 0 Comments
Charles Courtney Curran (American 1861-1942) Shadow Decoration. 1887, oil on canvas
March may have gone out like a lion; the nights may still be cold and the mountains of dirty plowed-up snow still not entirely melted away; the flowers and buds may still be hanging back timidly after a long and difficult winter. But spring is here nonetheless – and the way that we can tell, when all other measures fail, is by the lengthening daylight. It lifts our SADdened spirits, even when somewhat obscured by April's oft-rainy skies.
Simply put, we sighted humans crave the light. It doesn't just show us what's in our environment and how to navigate it safely; it has a profound psychological effect on us as well. In the visual arts, of course, light has always played a crucial role, pointing our attention at whatever it is that the artist wishes to emphasize and shaping our emotional reaction to that focal image. But the ways in which artists have manipulated light, both in terms of stylistic approach and the media available to them, have changed radically over time.
We think of chiaroscuro – the deliberate creation of stark contrasts between light and dark areas – as predominantly a Renaissance Italian painting technique, for example; but it also manifested in woodcuts, and probably its most famous practitioner in paint was Rembrandt, several centuries later. It took a whole new turn in modern times with the invention of photography and cinematography. The approach to shading that contemporary artists refer to as "light modeling" was known as far back as the skiagraphia of the Athenian painter Apollodoros in the fifth century BCE, appearing again in Macedonian mosaics and Roman and medieval manuscript illumination. Tenebrism – nocturnal scenes lit only by candlelight or firelight – became popular in Spanish art and is closely associated with the works of Caravaggio and Rubens; but it surfaced again in the 20th century, transformed by urban electrification, in the moody neon-lit works of the likes of Edward Hopper.
A fascinating overview of the historical progression of the use of different types of light in art will be unveiled this Friday, April 11 at the Frances Lehman Loeb Art Center on the Vassar College campus. Touted as the first exhibition of its kind, "Mastering Light: From the Natural to the Artificial" explores artistic responses to light by European and American artists from the 16th through the early 20th centuries.
The artworks included in "Mastering Light" are divided up into three sections based on the type of illuminated employed: "Natural Light," "Nocturnal Light" and "Artificial Light." The Lehman Loeb will capitalize on its strong Rembrandt collection by including his works in all three categories. Other highlights (no pun intended) will be a Dürer engraving, Saint Jerome in His Study; a Tenebrist Goya etching of a starlit witches' Sabbat; one of Hogarth's 18th-century political etchings; Charles Courtney Curran's 1887 oil Shadow Decoration; a Toulouse-Lautrec lithograph; two Edvard Munchs, a painting and a woodcut; Joseph Stella's 1914 oil of Coney Island, Battle of Lights, on loan from the Museum of Modern Art; and Hopper's 1921 etching Night Shadows. Visitors can also catch a projection 51 seconds of movie film shot by Thomas Edison at night at the 1901 Pan-American Exposition, which introduced electric lighting to the American public.
The kickoff for the exhibition will be a talk by William C. Sharpe, professor of English at Barnard College and author of New York Nocturne: The City after Dark in Literature, Painting and Photography, 1850-1950, winner of the 2009 Modernist Studies Association Book Prize. The lecture will take place in Taylor Hall, Room 102, beginning at 5:30 p.m. on Friday, April 11 and be followed by a 6:30 p.m. reception in the Atrium of the Art Center.
"Mastering Light" will be up at the Lehman Loeb through June 29. Two events later this month involving the new exhibition include a Gallery Talk by curator Patricia Phagan at 4 p.m. on Thursday, April 24 and Family Day artmaking activities and tours geared to kids aged 5 to 10 years on Saturday, April 26 from 1:30 to 4 p.m. No registration required to participate in Family Day, and all these events are free and open to the public.
"Artists are drawn to shifting light effects, and they frequently edit and exaggerate and experiment with them in pictorial images, creating their own illusions of natural light with symbolic and emotional moods and meanings," says Phagan. "Overall, these works show that light can connote deeper meanings: symbolic, moral, intellectual or nationalistic." The artists included in the exhibition that she curated, she says, "left us with not only arresting works of art, but also with a deeper understanding of aesthetic, social and technological histories of lighting."
The Frances Lehman Loeb Art Center is open from 10 a.m. to 5 p.m. on Tuesday, Wednesday, Friday and Saturday, from 10 a.m. to 9 p.m. on Thursday and from 1 to 5 p.m. on Sunday. For more information about "Mastering Light: From the Natural to the Artificial," call (845) 437-5632 or visit https://fllac.vassar.edu/exhibitions/2014/mastering-light.html.
"Mastering Light: From the Natural to the Artificial" opening, Friday, April 11, 5:30 p.m., free, Frances Lehman Loeb Art Center, Vassar College, 124 Raymond Avenue, Poughkeepsie; (845) 437-5632, https://fllac.vassar.edu.
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Help Build a Community Center for Unhoused Youth
$4,600 raised of $100,000 goal •
Kathleen Campbell
Sheila Campbell
Harriet Rose
Blake Thomas and Amit Cohen are organizing this fundraiser to benefit Youth Spirit Artworks.
Want to join us in making a difference in the lives of disadvantaged Bay Area youth? Your donation will help make the SEAD Center a reality!
We're about to begin construction on the Sustainability Education and Arts Development (SEAD) Center — a hybrid studio and living space that will serve residents of Youth Spirit Artworks' (YSA) tiny house village for unhoused youth. YSA is a local nonprofit that serves unhoused and low-income Bay Area youth. Their tiny home village in South Oakland provides 22 residents aged 18-24 with housing, arts training, and access to essential services. Since 2007, more than 500 YSA program graduates have received a high school diploma, entered college, or entered the workforce.
Keep reading to learn how the SEAD Center will help mark the latest chapter in YSA's mission to serve.
SHAC team photo, fall 2022
But first, who are we?
We are Sustainable Housing at Cal (SHAC), a multidisciplinary group of students at UC Berkeley who share the common goal of creating sustainable solutions to housing issues. Since the fall of 2021, our Solar Decathlon team has partnered with youth, YSA staff, and professional mentors to design the SEAD Center and fund its construction.
Rendering of the SEAD Center in the existing tiny house village
The SEAD Center will serve, first and foremost, as a community space for education and the arts. The 1500 sq ft building will be used as a workshop, art studio, and study area. The center will also include a space for someone to make their home. We intend to house visiting artists and professionals who will run training workshops for the village residents — while living among them! This model of reciprocal community living is central to the values expressed by youth and YSA staff at the onset of the project.
The center will be located adjacent to YSA's existing tiny house village and will anchor a major new expansion of its housing. Led by our partners at the University of San Francisco, the expansion includes around 24 redesigned tiny homes, with the SEAD Center located at their nexus. The project will be critical to helping YSA expand its housing stock and bolster its capacity to provide services to marginalized youth.
YSA fine art studio & member meeting
The project's design was developed in close partnership with YSA staff and youth. Through weekly meetings with village residents and staff, the team identified critical programmatic and design goals and learned more about life in the village. These meetings form the foundation for our design as we aim to center the youth's lived experiences. The design adheres to a model of cooperative living and promotes education, self-responsibility, and a sense of community — all key values identified by the youth.
Since its inception, creating an ambitious sustainable design has been a top priority for the SEAD Center. Our most crucial sustainable endeavor is the integration of passive design elements which can serve occupants — without needing electricity! These include south-facing windows that maximize daylight and natural heat gain in the winter, significantly reducing overall energy use. Meanwhile, strategic roof overhangs block the direct summer sun, providing energy-free cooling from the shade. Smart, passive designs like these reduce environmental impact and minimize operating costs for YSA.
SEAD's solar array will cover electricity needs, further reducing operating costs and making the center resilient to blackouts. Resiliency is crucial to our other sustainable features: water recycling and rainwater harvesting. The center plans to recycle gray water from the shower to save the building over 3,500 gallons of water per year. Furthermore, our highly efficient, low-flow fixtures will save over 4,300 gallons per year.
Because of our strong focus on sustainability, the project will serve as UC Berkeley's latest entry into the U.S. Department of Energy Solar Decathlon — a collegiate competition that challenges student teams to design and build highly efficient buildings powered by renewables. The guiding principles of the Solar Decathlon helped inform the SEAD Center's resilient and self-sufficient design, ensuring it serves residents for decades to come.
SHAC team engaging village residents
WHERE WILL YOUR MONEY GO
The construction phase of our project is approaching soon. Your generous donations will allow us to purchase vital materials such as framing, insulation, and roofing.
Here's what your donations can accomplish!
$10 = 1 sq ft of flooring
$45 = 1 sq ft of countertop
$65 = 1 sq ft of window pane
$150 = bathroom fan
$385 = low-flow toilet
$450 = 1 wood cabinet
$2000 = electric water heater
$3000 = 1000 watts of solar energy per year
$4600 = atmospheric water generator
$23,000 = battery and solar inverter
Donors will also receive the following rewards for their contributions:
Every donation will play a crucial part in making SEAD Center a reality!
Donors will be proud to know they made a difference in the lives of disadvantaged Bay Area youth AND contributed to a valuable experience for Berkeley students.
Fundraising team (2)
Blake Thomas
Youth Spirit Artworks
Registered nonprofit
Donations are typically 100% tax deductible in the US.
Amit Cohen
Raised $700 from 4 donations
Created October 30, 2022October 30, 2022


Shopping for low cost homeowners insurance in Chatham, VA does not have to be difficult. We are here to help you find and compare multiple providers. Simply enter your Zip in the form above and you will be taken to a page which will list the top most reputable home insurance companies in your Pittsylvania county.
The coverage mentioned above is a basic form of coverage that you absolutely need to have. There are optional coverage items that you can add, such as guaranteed replacement cost, which provides the most complete coverage. If your house gets totally damaged, the insurance company will pay for the cost of building it. However, as you might expect, most insurers require you to meet specific underwriting requirements and pay a higher premium. This brings us to another important point: How much does it cost to insure your home in Chatham, VA?
To get cheap Chatham, VA home insurance quotes use our simple comparison tool and you will be ahead of most regular consumers who do not do their own comparison or rely on an agent to do it for them.
Catastrophe can strike anyplace, at any time. That is why it is so critical that your property is insured. You by no means know when something could come about to it, so you want to be ready need to anything take place. In the pursuing post, you are likely to be given tips that will aid you to be completely ready.
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Ansel Adams Exhibit at the Arlington Museum of Art
The Arlington Museum of Art (AMA) will be hosting an amazing exhibit, Ansel Adams: Masterworks, featuring over 45 quintessential images by famed American photographer Ansel Adams. The exhibit will be on display May 3 through August 3. An opening reception with a preview for exhibit sponsors, museum members and special guests will be held Friday, May 2, 2014 from 6:00 to 8:00 p.m.
In a career that spanned more than five decades, Ansel Adams (1902-1984) became one of America's most beloved photographers. There are few artists whose name and work represent the extraordinary level of recognition and artistic achievement as his. Adams profoundly influenced the course of 20th century photography, not only in his rich, technically precise images, but also through his efforts to advance photography as an art form. As an artist, educator, and writer, he helped establish many of the institutions that have come to represent the highest aspirations of the medium of photography. As an innovator, he developed techniques that became the basis for cutting edge photography of the future.
Aside from his almost unparalleled success as a photographer and an artist, Adams' relished his role as a champion for environmental causes. He used the platform with which he was most familiar, photography, to bring the American landscape, both wild and civilized, to the forefront of the national consciousness, and his devotion to promoting the preservation of the American landscape is evident in his poignant and reverent work. From the pristine hidden corners of the American National Parks System, to the stark, gritty reality of the ravages of the Great Depression, Adams' work gave a voice to the fabric of this country through images of its land and its people.
AMA executive Director Chris Hightower spoke about the broad appeal of the artist and his work, "Ansel Adams was an American icon for many different reasons. He had the eye of an artist and the heart of an environmentalist, both of which were captured through his lens." Accompanying this exhibit will be related programming including a lecture and video series, demonstrations, and workshops.
AMA is located at 201 West Main Street, Arlington, TX 76010. Admission tickets are available online, or may be purchased at the door.
Labels: Ansel Adams exhibit, Arlington Museum of Art, black and white photography, landscape photography, photography
Community Bands to Play at UTA - May 3, 2014
Meals on Wheels 40th Anniversary Gala
Rachmaninoff Concert by Timeless Concerts


Here are some recordings of some of Club Red CEO, coach and author, Tony Inman's radio interviews.
In this fascinating chat, Tony outlines the importance of seeing the concept of change, not as something to fear, but as something to embrace. We live in a world of rapid change, so you either embrace it or fall behind.
In this radio interview, Tony explains how you can truly harness the Law of Attraction to create the business you want, so that you can ultimately create the lifestyle you want.
In this conversation, Tony reveals the importance of looking at your business through the eyes of your customers and looking for those extra ways of ensuring that you provide a great customer experience.
Tony acts as the interviewer in this radio interview and prompts Michael to reveal some of the secrets of success that he has learned on his amazing business journey that has brought him to the world of radio.
If you'd like more information on any of these topics, please contact Tony.


Superdata's monthly figures are out for digital gaming sales in September. The highlight is the apperance of Uncharted: The Lost Legacy in the Top 10, having taken the number four sport with 1.44m. With no adds-on or additional content available, and a selling price of 30 we can easily calculate a figure of 48,000 sold over the month.
It's rare that we get a glimpse at a clean digital sales figure like this – as often it's impossible to pick apart microtransactions from full game sales in the figures provided.
It would then be great to tell you what the total number of sales were, or even just the ratio of physical to digital sales. We have the sales data for UK physical in front of us, after all, but to do so would easily allow anyone to calculate the actual physical sales figure and that would break our agreement with Ukie, GfK and Sony not to publish such figures.
What we can say is that across the month, the title had a significant percentage of digital to physical sales – which isn't very helpful to anyone who wants to know how well the franchise spin-off performed overall. We can certainly stretch to saying that physical sales are still higher than digital sales – though that won't be much of a surprise to anyone.
So, another month, and another frustrating dance around the real numbers.
As for the rest of the Top Ten, we see FIFA still wracking up impressive figures on the eve of its next release, and the outside chance of seeing three FIFA games in the Top Ten next month, plus Battlefield 1 for EA as well. Ubisoft's Tom Clancy titles continue to earn well for the company, while Activision shifted around 25,000 more units ofCrash Bandicoot N. Sane Trilogy digitally.


You should shortly recieve a confirmation email. Please ensure that you keep your contact details up to date with us. If for any reason you can no longer attend please let us know via email at info@carrerinteractive.org so that your place can be made available for someone else.
Due to the popularity of this event, we may not be able to admit you on the day if you have not booked a free ticket. If you have any difficulty booking your ticket please email info@careerinteractive.org with the header 'Autumn Fair' and we will send your ticket.
I'm happy to receive news, career advice and updates from Career Interactive.


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Clothes Show goes dance
The Dance Show, held at Birmingham NEC on December 3–5, promises live performances, dance classes, seminars, masterclasses and awards.
Running alongside fashion and beauty event Clothes Show Live, The Dance Show's main stage will present performances, including appearances from the stars of "So You Think You Can Dance", including Charlie Bruce and Robbie White, and "Got To Dance". It also has four purpose-built dance studios, where visitors can learn styles from Egyptian dance to burlesque, swing, samba and West End routines. Arlene Phillips will make a special appearance on December 3, leading the judging panel for the Young Dancer of the Year award, sponsored by Spotlight and supported by Dancers Inc, Dance Xchange and CDET. Rambert Dance Company is among the companies giving masterclasses. The show also features hundreds of leading dance exhibitors, including Bloch and Katz Dancewear. Across the weekend, there will be Q&A sessions giving advice on getting into dance schools, groups and projects, while dance directory Spotlight and the performers' trade union Equity will be available to advise dancers hoping to develop their careers. For more information, see thedanceshow.co.uk.
Simon Oliver
Simon Oliver has been production editor of Dancing Times since 2010 and is highly experienced in design across print and online magazine production. Throughout his career, Simon has worked on a diverse range of subjects including music, family history, book collecting and poker.


How has the government made self-employment so attractive?
// // <meta http-equiv="refresh" content="0; URL=/?_fb_noscript=1″ /> Bernie Sanders and the socialists can never get it right. There is nothing more demeaning than giving something to someone he or she knows is undeserved. It diminishes the person is his own eyes and impacts his self-worth. At least FDR created the WPA, where people could earn a living and feel the pride of accomplishment.
Why do businesses so often fail to understand the value of people?
People who experience economically or technologically driven endings to their work source may transfer their skills to a new area of endeavor. However, those who do so with a willingness and a joy for so doing, become transformed by seeing their work from another perspective and truly become enriched by the transformation.
Gain greater understanding by reading Using Your Inner Power to Find Meaningful Work, now available in print or eBook from Amazon. Or contact http://www.yorkinc.com.
Why do people desire to work for themselves?
People who seek self-employment options do not do so primarily to make money. They do so primarily to be free; free from the frustrations and aggravations so often associated with the bureaucracy of the corporate world. However, freedom is not free and one who desires freedom must be willing to pay the price, which means working with a level of commitment and determination that exceeds that characterized by the average job. It's not easy, but it's worth it.