The open Bose-Hubbard chain: Pseudoclassical approach

We analyze stationary current of bosonic carriers in the Bose-Hubbard chain of length $L$ where the first and the last sites of the chain are attached to reservoirs of Bose particles acting as the particle source and sink, respectively. The analysis is curried out by using the pseudoclassical approach which reduces the original quantum problem to the classical problem for $L$ coupled nonlinear oscillators. It is shown that an increase of oscillator nonlinearity (which is determined by the strength of inter-particle interactions) results in a transition from the ballistic transport regime, where the stationary current is independent of the chain length, to the diffusive regime, where the current is inverse proportional to $L$.