Superdiffusion, normal diffusion, and chaos in semiclassical Bose-Hubbard chains

We study the evolution of two-point correlation functions of the one-dimensional Bose-Hubbard model in the semiclassical regime in the framework of truncated Wigner approximation with quantum jumps as first-order corrections. At early times, the correlation functions show strong superdiffusion with universal integer exponents determined solely by the initial conditions and completely insensitive to system parameters and chaos. Only after a long time does this regime crosse over to the normal diffusion regime which is most robust when nonintegrability is strong. For strong nonintegrability, the system ends up in a homogeneous state, while for weak nonintegrability, the oscillations and inhomogeneities persist, despite the fact that chaos is nearly always strong and only weakly depends on the nonintegrability parameter. We conclude that the superdiffusive regime is neither prethermalized nor a precursor to thermalization but an early-time phenomenon related to a special scaling symmetry of the Bose-Hubbard Hamiltonian.