Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices

Abstract

We study numerically time evolution in classical lattices with weak or moderate nonlinearity which leads to interactions between linear modes. Our results show that in a certain strength range a moderate nonlinearity generates a dynamical thermalization process which drives the system to the quantum Gibbs distribution of probabilities, or average oscillation amplitudes. The effective dynamical temperature of the lattice varies from large positive to large negative values depending on the energy of the initially excited modes. This quantum Gibbs distribution is drastically different from the usually expected energy equipartition over linear modes corresponding to a regime of classical thermalization. Possible experimental observations of this dynamical thermalization are discussed for cold atoms in optical lattices, nonlinear photonic lattices and optical fiber arrays.

Dynamics and thermalization of a Bose-Einstein condensate in a Sinai-oscillator trap

“…2 for the dependence E m ) so that we can expect chaos and thermalization to be set in at δE β > ∆E, thus leading to β c ∼ 1. Indeed, similar estimates have been confirmed in systems of coupled nonlinear oscillators [24,35,36]).…”

“…The dynamical thermalization in nonlinear chains with disorder has been studied in [34,35] where it was shown that the quantum Gibbs distribution appears in an isolated system above a certain border of nonlinearity β > β c . The dynamical thermalization for the GPE in a chaotic Bunimovich billiard has been established in [7].…”

Dynamical thermalization in Bose-Hubbard systems

“…This feature has been noted and used for nonlinear chains with disorder [31,32] and Bose-Einstein condensates, described by the GrossPitaivskii equation, in chaotic two-dimensional billiards [33]. It is interesting to note that in these nonlinear systems [31][32][33] the DTC is still valid but it is induced by a nonlinear mean-field interactions between linear states. (12) where β and µ were chosen such that k n k = N = 8 and k E k n k + N 2 U/L = Eα with Eα/N corresponding to the centers of the abscissa intervals (e.g.…”

Wave condensation with weak disorder versus beam self-cleaning in multimode fibers

“…As will be discussed throughout this paper, these simulations reflect the discrete nature of the resonance manifold underlying wave turbulence in MMFs. We note that understanding the mechanisms that can freeze the process of thermalization is an important problem that is currently analyzed in various systems, such as, e.g., finite size effects in discrete or mesoscopic wave turbulence [55][56][57][58][59][60][61][62][63][64][65][66], in Fermi-Pasta-Ulam chains [78][79][80][81][82], or in nonlinear disordered systems [83,84]. ...…”