Related papers: Ergodic theorems in quantum probability: an applic…
We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\in(0,1)$. A general framework is constructed to make precise the notions of…
This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand…
It has been shown that in one dimension the environment viewed by the particle process (EVP process) in quasi periodic random environment is uniquely ergodic and mixing under mild additional assumptions. Here we construct an analytic quasi…
Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given "performance" function. For a continuous self-map of a compact metric space and a dense set of continuous…
There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…
We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic…
The connection between the non-equilibrium dynamics of isolated quantum many-body systems and statistical mechanics is a fundamental open question. It is generally believed that the unitary quantum evolution of a sufficiently complex system…
We prove strengthenings of the Birkhoff Ergodic Theorem for weakly mixing and strongly mixing measure preserving systems. We show that our pointwise theorem for weakly mixing systems is strictly stronger than the Wiener-Wintner Theorem. We…
We study the ergodic properties of two classes of random dynamical systems: a type of Markov chain which we call the \textit{alternating random walk} and a certain stochastic billiard system which describes the motion of a free-moving rough…
The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian motion with a linear drift as a stationary distribution (modulo additive constants). We show that these solutions are attractive, a result known as a…
We give two formulations of exclusion statistics (ES) using a variable number of bosonic or fermionic single-particle states which depend on the number of particles in the system. Associated bosonic and fermionic ES parameters are…
We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein,…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively…
We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…
Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…