Related papers: Markov Diagrams for Some Non-Markovian Systems
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear…
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the…
In literature on stochastic thermodynamics it is stated that for a system connected to multiple thermal reservoirs, the transition rates between two energy levels equals the sum of transition rates corresponding to each thermal bath the…
It is believed that an isolated and far-from-equilibrium quantum many-body system should try to attain equilibrium via a mechanism whereby any given subsystem acts as an open quantum system that is coupled to an environment, which is the…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
We present a formalism for detection of non-Markovianity through uncertainty relations. We show that when there is an information back-flow to the system from its environment through CP-divisibility breaking, the Choi-states corresponding…
The nonequilibrium response and fluctuations of Markovian systems, both near and far from equilibrium, are best understood by varying their parameters along dynamical equivalence classes. In this note, I illustrate this approach for an…
Recently, a large class of quantum non-Markovian piecewise dynamics for an open quantum system obeying closed evolution equations has been introduced [B. Vacchini, Phys. Rev. Lett. 117, 230401 (2016)]. These dynamics have been defined in…
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…
A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions…
We study Markov processes with values in the space of general two-dimensional arrays whose distribution is exchangeable. The results of this paper are inspired by the theory of exchangeable dynamical random graphs developed by H. Crane…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
The study of quantum dynamics featuring memory effects has always been a topic of interest within the theory of open quantum system, which is concerned about providing useful conceptual and theoretical tools for the description of the…
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…
We show how to use symbolic dynamics of Schreier graphs to embed the Grigorchuk group into a simple torsion group of intermediate growth and to construct uncountably many growth types of simple torsion groups.