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 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.

15 pages, 12 figures. Small modifs., video abstract 107MB at http://www.quantware.ups-tlse.fr/dima/video/gibbs2013.mp4

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• Dynamical thermalization in isolated quantum dots and black holes
• Dynamical thermalization of Bose-Einstein condensate in Bunimovich stadium
• Dynamics and thermalization of Bose-Einstein condensate in Sinai oscillator trap
• Dynamical thermalization in Bose-Hubbard systems
• Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole
• Kolmogorov turbulence defeated by Anderson localization for a Bose-Einstein condensate in a Sinai-oscillator trap