Related papers: Ergodic theory of multi-layer interacting particle…
A simple argument shows that eigenstates of a classically ergodic system are individually ergodic on coarse-grained scales. This has implications for the quantization ambiguity in ergodic systems: the difference between alternative…
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena…
Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum…
We investigate one-dimensional driven diffusive systems where particles may also be created and annihilated in the bulk with sufficiently small rate. In an open geometry, i.e., coupled to particle reservoirs at the two ends, these systems…
There is studied an invariant measure structure of a class of ergodicl discrete dynamical systems by means of the measure generating function method
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…
In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.
We study a classical multiparticle system (such as Toda lattice) whose dynamics we intend to control by forces applied to few particles of the system. Various problem settings, typical for control theory are posed for this model; among…
Based on the classical and quantum ergodic hierarchy, a framework for mixed systems with a phase space composed by two uncorrelated integrable and chaotic regions is presented. It provides some features of mixed systems connecting the…
Multiscale thermodynamics is a theory of relations among levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case but it is applicable to both static and time evolving processes in…
In this work, we introduce a unified method to characterize and measure multipartite entanglement using the framework of thermodynamics. A family of the new entanglement measures is proposed: \textit{ergotropic-gap concentratable…
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic…
In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down…
Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic,…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…