Related papers: Markov Diagrams for Some Non-Markovian Systems
We study Markovian and non-Markovian behaviour of stochastic processes generated by $p$-adic random dynamical systems. Given a family of $p$-adic monomial random mappings generating a random dynamical system. Under which conditions do the…
We study the quantum dynamics of a many-body system subject to coherent evolution and coupled to a non-Markovian bath. We propose a technique to unravel the non-Markovian dynamics in terms of quantum jumps, a connection that was so far only…
The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme…
Examples of the construction of Hamiltonian structures for dynamical systems in field theory (including one reputedly non-Hamiltonian problem) without using Lagrangians, are presented. The recently developed method used requires the…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
In this paper we introduce and develop the theory of non-autonomous graph directed Markov systems which is a generalization of the theory of conformal graph directed Markov systems of Mauldin and Urba\'nski, first presented in their book,…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual…
Non-Markovian effects in open quantum system dynamics usually manifest backflow of information from the environment to the system, indicating complete-positive divisibility breaking of the dynamics. We provide a criterion for witnessing…
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
We unveil a novel source of non-Markovianity for the dynamics of quantum systems, which appears when the system does not explore the full set of dynamical trajectories in the interaction with its environment. We term this effect…
Complex systems may often be characterized by their hierarchical dynamics. In this paper do we present a method and an operational algorithm that automatically infer this property in a broad range of systems; discrete stochastic processes.…
An all-optical scheme for simulating non-Markovian evolution of a quantum system is proposed. It uses only linear optics elements and by controlling the system parameters allows one to control the presence or absence of information backflow…
We provide an analysis on non-Markovian quantum evolution based on the spectral properties of dynamical maps. We introduce the dynamical analog of entanglement witness to detect non-Markovianity and we illustrate its behaviour with several…
Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the…
We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.
Open quantum systems (OQS) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. Here, we give an overview of some of the most important techniques available to…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…