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

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.

💡 Research Summary

This paper investigates the self‑thermalization dynamics of the M‑site Bose‑Hubbard (BH) model using a pseudoclassical (or “pseudo‑classical”) approach, and it extends the analysis to non‑equilibrium steady‑state particle transport across a short lattice coupled to two BH reservoirs. The authors first rewrite the BH Hamiltonian in both Wannier (site) and Bloch (momentum) representations, highlighting the two integrable limits (U = 0, J ≠ 0 and J = 0, U ≠ 0) and the generic chaotic regime where both hopping J and interaction U are finite. In the chaotic regime the many‑body spectrum follows a Wigner‑Dyson distribution, indicating quantum chaos.

The central object of study is the single‑particle density matrix (SPDM) ρ_{k,k′}(t)=Tr