Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians

TL;DR

This paper provides a broad and accessible explanation of how lattice models of fermions or bosons with quadratic Hamiltonians relax to gaussian and generalized Gibbs states, including in time-dependent and periodically driven systems.

Contribution

It introduces a general, semi-quantitative framework for understanding relaxation in quadratic lattice models, applicable to arbitrary initial states with mild correlation conditions.

Findings

Relaxation to gaussian and generalized Gibbs states is explained for quadratic lattice models.

The approach applies to time-dependent and Floquet systems.

Conditions on initial states for relaxation are identified.

Abstract

We present an elementary, general, and semi-quantitative description of relaxation to gaussian and generalized Gibbs states in lattice models of fermions or bosons with quadratic hamiltonians. Our arguments apply to arbitrary initial states that satisfy a mild condition on clustering of correlations. We also show that similar arguments can be used to understand relaxation (or its absence) in systems with time-dependent quadratic hamiltonians, and provide a semi-quantitative description of relaxation in quadratic periodically driven (Floquet) systems.