Microscopic models of source and sink for atomtronics

We analyze microscopic models of the particle source or sink which consist of a one- or two-site Bose-Hubbard model (the system) weakly coupled to a many-site Bose-Hubbard model (the reservoir). Assuming unequal filling factors for the system and reservoir, we numerically study equilibration dynamics and compare it with the solution of the master equation on the reduced density matrix of the system. Necessary conditions for the validity of the master equation approach are formulated.