Analysis of self-thermalization dynamics in the Bose-Hubbard model by using the pseudoclassical approach

TL;DR

This paper investigates the self-thermalization process in the Bose-Hubbard model using a pseudoclassical approach, revealing that weak interactions lead to thermalization and that coupled systems equilibrate to a common thermal state, with results matching master equation predictions.

Contribution

It demonstrates that weak interactions induce chaos without significantly altering the thermal density matrix, and shows coupled Bose-Hubbard systems relax to the same thermal state, with numerical results aligning with master equation solutions.

Findings

Weak interactions cause chaos but preserve thermal density matrix.

Coupled systems equilibrate to a common thermal state.

Numerical current matches master equation predictions.

Abstract

We analyze the self-thermalization dynamics of the $M$-site Bose-Hubbard model in terms of the single-particle density matrix that is calculated by using the pseudoclassical approach. It is shown that a weak inter-particle interaction, which suffices to convert the integrable system of non-interacting bosons into a chaotic system, has a negligible effect on the thermal density matrix given by the Bose-Einstein distribution. This opens the door for equilibration where the two coupled Bose-Hubbard systems, which are initially in different thermal states, relax to the same thermal state. When we couple these two subsystems by using a lattice of the length $L\ll M$, we numerically calculate the quasi-stationary current of Bose particles across the lattice and show that its magnitude is consistent with the solution of the master equation for the boundary driven $L$-site Bose-Hubbard model.