Related papers: Non-Commutative Markov Chains and Multi-Analytic O…
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of…
Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to…
Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a key role in reachability analysis…
Model checking has been successfully applied to verification of computer hardware and software, communication systems and even biological systems. In this paper, we further push the boundary of its applications and show that it can be…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
Exchange of information between a quantum system and its surrounding environment plays a fundamental role in the study of the dynamics of open quantum systems. Here we discuss the role of the information exchange in the non-Markovian…
In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…
We study the behavior of non-Markovianity with respect to the localization of the initial environmental state. The "amount" of non-Markovianity is measured using divisibility and distinguishability as indicators, employing several schemes…
Transfer operators have been used widely to study the long time properties of chaotic maps or flows. We describe quantum analogues of these operators, which have been used as toy models by the quantum chaos community, but are also relevant…
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact that, due to interactions between a quantum open system and its surrounding environment, information about the system can be spread redundantly…
In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. The quantum Markov chain, like the classical Markov chain, is a fundamental tool for the investigation of the basic properties such…
The model of multi-level open quantum system interacting with a non-vacuum reservoir in the rotating wave approximation is considered. We provide an exact integral representation for the reduced density matrix of the system. For identical…
We study the interaction between several fields initially in coherent states. The solution allows us to explain why coherent states remain coherent states when subject to non-Markovian dissipation. We first study the interaction between two…
In this note we consider a Markov chain formed by a finite system of interacting birth-and-death processes on a finite state space. We study an asymptotic behaviour of the Markov chain as its state space becomes large. In particular, we…
We present a scattering approach for the study of the transport and thermodynamics of quantum systems strongly coupled to their thermal environment(s). This formalism recovers the standard non-equilibrium Green's function expressions for…
We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of…
We present a multichannel model for elastic interactions, comprised of an arbitrary number of coupled finite square-well potentials, and derive semi-analytic solutions for its scattering behavior. Despite the model's simplicity, it is…
Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the…