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 ring geometry using the single-particle density matrix calculated via the pseudoclassical approach. We show that a weak inter-particle interaction, which has a negligible effect on the thermal state given by the Bose-Einstein distribution, suffices to convert the integrable system of non-interacting bosons into a chaotic system. Next we consider two systems of weakly interacting bosons (i.e., two Bose-Hubbard systems) in different thermal states which are coupled by a point contact. We demonstrate that the chaotic nature of the Bose-Hubbard model ensures irreversible relaxation of both systems to global thermal equilibrium. Finally, substituting the point contact with a lattice of 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 system.