Transport in the Boundary-Driven Dissipative Bose-Hubbard Chain

Extending previous work on a periodically driven Bose-Hubbard chain with boundary dissipation, we characterize the transport properties in the non-equilibrium steady-state. Using the semiclassical truncated Wigner approximation (TWA), we find distinct regimes for the energy current as a function of the driving amplitude. For intermediary drive strengths, we observe a Resonant Nonlinear Wave regime where the current remains constant as the drive strength increases. For vacuum initial conditions, this steady-state plateau becomes unstable above a critical system-size. However, we identify different initial conditions under which the RNW solution remains stable up to numerically accessible system sizes, indicating that the system exhibits bistable behaviour even after quantum fluctuations are included.