# Relaxation to Gaussian Generalized Gibbs Ensembles in Quadratic Bosonic Systems in the Thermodynamic Limit

## TL;DR

This paper demonstrates that quadratic bosonic systems in the thermodynamic limit relax to Gaussian generalized Gibbs ensembles, revealing a general mechanism for equilibration based on diagonal singularity.

## Contribution

It introduces a universal mechanism explaining relaxation to GGEs in quadratic bosonic systems, including coupled systems, under certain physical conditions.

## Key findings

- Quadratic bosonic systems relax to Gaussian GGEs.
- Relaxation occurs from general initial states, not necessarily Gaussian.
- Explicit analytical demonstration for coupled harmonic oscillator systems.

## 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.