Dynamics of the Bose-Hubbard chain for weak interactions

We study the Boltzmann transport equation for the Bose-Hubbard chain in the kinetic regime. The time-dependent Wigner function is matrix-valued with odd dimension due to integer spin. For nearest neighbor hopping only, there are infinitely many additional conservation laws and nonthermal stationary states. Adding longer-range hopping amplitudes entails exclusively thermal equilibrium states. Especially for small next-nearest neighbor hopping amplitudes, we observe prethermalization with two time scales, which can be related to the relative strength of the nearest and next-nearest hopping. We provide a derivation of the Boltzmann equation based on the Hubbard Hamiltonian, including general interactions beyond on-site, and illustrate the results by numerical simulations.