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 Lll 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.