Dynamical Freezing of Relaxation to Equilibrium

Abstract

We provide evidence of an extremely slow thermalization occurring in the Discrete NonLinear Schrödinger (DNLS) model. At variance with many similar processes encountered in statistical mechanics -typically ascribed to the presence of (free) energy barriers -here the slowness has a purely dynamical origin: it is due to the presence of an adiabatic invariant, which freezes the dynamics of a tall breather. Consequently, relaxation proceeds via rare events, where energy is suddenly released towards the background. We conjecture that this exponentially slow relaxation is a key ingredient contributing to the non-ergodic behavior recently observed in the negative temperature region of the DNLS equation.

Condensation transition and ensemble inequivalence in the discrete nonlinear Schrödinger equation

“…Below this line no physical state is allowed, while a standard thermal phase extends in between these two lines: dynamics (2) makes any initial state eventually thermalize to energy equipartition. Above the β = 0 line numerical studies (e.g., see [4,6]) have shown that the hamiltonian dynamics of the DNLSE exhibits localized breather excitations. Such excitations can survive over extremely long times (exponentially long in their mass [6]) even in a chain made of a few tens of sites [4].…”

“…Above the β = 0 line numerical studies (e.g., see [4,6]) have shown that the hamiltonian dynamics of the DNLSE exhibits localized breather excitations. Such excitations can survive over extremely long times (exponentially long in their mass [6]) even in a chain made of a few tens of sites [4]. The coupling of the localized breathers among themselves, through the background energy fluctuations, is very weak and their coalescence into a single localized giant breather, even if possible (in fact, breathers are known to merge when they collide [4]), is practically unobservable.…”

Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

“…Using a recently derived approximation [51] for the integral equation (29), one can also check that the critical exponent for the correlation length coincides with the value from the universality class of the Ising model:…”

“…Hence we see that our models allow for substantial chaos to be built in at the lattice scale as advertised above. There could be also some adiabatic invariant slowing down the thermalization significantly, as recently investigated in [29].…”

Producing suprathermal tails in the stationary velocity distribution

“…Such an effect is often observed and, for obvious reasons, we refer to it as localization, ensuring (relative) stability of high energy regions. Recent examples and demonstrations are presented in [10][11][12][13].…”