Bose Hubbard model far from equilibrium

We study the nonequilibrium steady state of the Bose Hubbard model coupled to Lindblad reservoirs, using the density matrix renormalization group in operator space. We observe a transition from a flat particle density profile in the noninteracting limit to the linear profile with onset of the interparticle interaction. Analyzing the effect of coherent pumping on the nonequilibrium steady state we find a subspace which remains unaffected by the pumping in the noninteracting limit with the protection gradually diminishing due to interparticle interaction. In the equilibrium situation with one or more symmetric reservoirs we show analytically that the steady state of the system is a product state for any interaction strength. We also provide analytical results in the noninteracting limits, using the method of the third quantization in operator space.