  We study chaotic dynamics and anomalous transport in a Bose-Hubbard chain in
the semiclassical regime (the limit when the number of particles goes to
infinity). We find that the system has mixed phase space with both regular and
chaotic dynamics, even for long chains with up to hundred wells. The
consequence of the mixed phase space is strongly anomalous diffusion in the
space of occupation numbers, with a discrete set of transport exponents. After
very long times the system crosses over to the hydrodynamic regime with normal
diffusion. Anomalous transport is quite universal, almost completely
independent of the parameters of the model (Coulomb interaction, chemical
potential): it is mainly determined by the initial distribution of particles
along the chain. We corroborate our findings by analytical arguments: scaling
analysis for the anomalous regime and the Langevin equation for the normal
diffusion regime.
