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Relaxation to Gaussian generalized Gibbs ensembles in quadratic bosonic systems in the thermodynamic limit
Takaaki Monnai1, Shohei Morodome2, Kazuya Yuasa2
1Department of Materials and Life Science, Seikei University, Tokyo 180-8633, Japan.
Abstract:
Integrable quantum many-body systems are considered to equilibrate to generalized Gibbs ensembles (GGEs) characterized by the expectation values of integrals of motion. We study the dynamics of exactly solvable quadratic bosonic systems in the thermodynamic limit, and show a general mechanism for the relaxation to GGEs, in terms of the diagonal singularity. We show analytically and explicitly that a free bosonic system relaxes from a general (not necessarily Gaussian) initial state under certain physical conditions to a Gaussian GGE. We also show the relaxation to a Gaussian GGE in an exactly solvable coupled system, a harmonic oscillator linearly interacting with bosonic reservoirs.
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