相关论文: Computer-assisted proof of ergodicity breaking in …

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…

We consider a coupled top model describing two interacting large spins, which is studied semiclassically as well as quantum mechanically. This model exhibits variety of interesting phenomena such as quantum phase transition (QPT), dynamical…

Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…

The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional…

In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities,…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…

For one dimensional maps the trajectory scaling functions is invariant under coordinate transformations and can be used to compute any ergodic average. It is the most stringent test between theory and experiment, but so far it has proven…

Dynamical system properties give rise to effects in Statistical Mechanics. Topological index changes can be the basis for phase transitions. The Euler characteristic is a versatile topological invariant that can be evaluated for model…

For every positive integer $n\geq 2$, we introduce the concept of measure-theoretic $n$-sensitivity for measure-theoretic dynamical systems via finite measurable partitions, and show that an ergodic system is measure-theoretically…

This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time…

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

For a general attractive Probabilistic Cellular Automata on S Z d , we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A).…

Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…

This letter raises the possibility that ergodicity concerns might have some bearing on the signal-to-noise paradox. This is explored by applying the ergodic theorem to the theory behind ensemble weather forecasting and the ensemble mean.…

We study measurement-induced nonlinear dynamics generated by an iterated quantum protocol combining an entangling gate, a single-qubit rotation, and post-selection. For pure single-qubit inputs, a particular choice of the single-qubit…

We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…

We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…