Comment on "Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined" [arXiv:0810.3720]

In a recent paper Roux [Phys. Rev. A 79, 021608® (2009), arXiv:0810.3720] argued that thermalization in a Bose-Hubbard system, after a quench, follows from the approximate Boltzmann distribution of the overlap between the initial state and the eigenstates of the final Hamiltonian. We show here that the distribution of the overlaps is in general not related to the canonical (or microcanonical) distribution and, hence, it cannot explain why thermalization occurs in quantum systems.