Related papers: Nonergodicity and Central Limit Behavior for Long-…
Unraveling the mechanisms of ergodicity breaking in complex quantum systems is a central pursuit in nonequilibrium physics. In this work, we investigate a one-dimensional spin model featuring a tunable long-range hopping term, $H_{n}$,…
The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…
We investigate the probability density of rescaled sum of iterates of sine-circle map within quasi-periodic route to chaos. When the dynamical system is strongly mixing (i.e., ergodic), standard Central Limit Theorem (CLT) is expected to be…
We study chaos in the Hamiltonian Mean Field model (HMF), a system with many degrees of freedom in which $N$ classical rotators are fully coupled. We review the most important results on the dynamics and the thermodynamics of the HMF, and…
Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of $N$ globally coupled particles moving on…
An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…
The core-halo approach of Levin et al.\ [Phys.\ Rep.\ {\bf 535}, 1 (2014)] for the violent relaxation of long-range interacting systems with a waterbag initial conditions is revisited for the case of the Hamiltonian Mean Field model. The…
We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or…
The nonequilibrium dynamics in chaotic quantum systems denies a fully understanding up to now, even if thermalization in the long-time asymptotic state has been explained by the eigenstate thermalization hypothesis which assumes a universal…
We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ: the independence of the Lyapunov spectrum…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
The dynamics of one parameter diagonal group actions on finite volume homogeneous spaces has a partially hyperbolic feature. In this paper we extend the Liv\v{s}ic type result to these possibly noncompact and nonaccessible systems. We also…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie…
Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick (LMG)…
We apply the mode coupling theory (MCT) which was recently worked out for molecular liquids to a liquid of diatomic, rigid molecules. Using the static correlators from a molecular dynamics simulation, we have solved the MCT-equations for…
We discuss the dynamics and thermodynamics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system to the canonical description of a stochastically forced Brownian system. We…
Computer simulations were used to study the gel transition occurring in colloidal systems with short range attractions. A colloid-polymer mixture was modelled and the results were compared with mode coupling theory expectations and with the…
Non-Hermitian systems are widespread in both classical and quantum physics. The dynamics of such systems has recently become a focal point of research, showcasing surprising behaviors that include apparent violation of the adiabatic theorem…