Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices

TL;DR

This study demonstrates that classical nonlinear lattices can dynamically thermalize to a quantum Gibbs distribution, with the effective temperature depending on initial conditions, contrasting classical energy equipartition.

Contribution

It reveals a novel dynamical thermalization process in classical lattices leading to quantum Gibbs distribution, bridging classical nonlinear dynamics and quantum statistical mechanics.

Findings

Moderate nonlinearity induces quantum Gibbs distribution in classical lattices.

Effective temperature varies from positive to negative based on initial energy.

Quantum Gibbs distribution differs from classical energy equipartition.

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 energy of initially excited modes. This quantum Gibbs distribution is drastically different from 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.