Current in open quantum systems

The study of dispersive current component which is present in the dynamics generated by a Liouville master equation was discussed. The study suggests that the dissipative component originates from coarse graining in time, implicit in a master equation and needs to be included to preserve current continuity. The explicit expression was derived for the dissipative current in the context of Markov approximation. It was observed that the new approach is illustrate with a simple numerical example, in which a quantum particle is coupled to a harmonic phonon bath and dissipation is described by the Pauli master equations.