Related papers: Thermalisation for Small Random Perturbations of D…
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems $(X^\varepsilon_t(x))_{t\geqslant 0}$ with $\varepsilon$-small additive L\'evy noise and initial…
A critical transition for a system modelled by a concave quadratic scalar ordinary differential equation occurs when a small variation of the coefficients changes dramatically the dynamics, from the existence of an attractor-repeller pair…
In this article, we provide detailed analysis of the long-time behavior of the underdamped Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise dynamical system converges to its unique attractor. We…
We investigate a one-dimenisonal Hamiltonian system that describes a system of particles interacting through short-range repulsive potentials. Depending on the particle mean energy, $\epsilon$, the system demonstrates a spectrum of kinetic…
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…
Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor…
The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…
Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…
We study, both numerically and analytically, the development of equilibrium after preheating. We show that the process is characterised by the appearance of Kolmogorov spectra and the evolution towards thermal equilibrium follows…
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression…
The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of chains are believed to exhibit cutoff, and yet establishing this fact is often…
Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…
The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
We investigate the mixing properties of a finite Markov chain in random environment defined as a mixture of a deterministic chain and a chain whose state space has been permuted uniformly at random. This work is the counterpart of a…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
We prove that certain asymptotic moments exist for some random distance expanding dynamical systems and Markov chains in random dynamical environment, and compute them in terms of the derivatives at the $0$ of an appropriate pressure…
We highlight a dynamical anomaly in which the rate of relaxation towards thermal equilibrium in a bi-partite quantum system violates the standard linear-response (Kubo) formulation, even when the underlying dynamics is highly chaotic. This…