  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. 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. In particular, convergence to thermal
equilibrium states with negative temperature is investigated.
