Current in open quantum systems

TL;DR

This paper reveals a dissipative current component in open quantum systems' dynamics, derived explicitly under the Markov approximation, emphasizing its role in current continuity and illustrating with a quantum particle coupled to a phonon bath.

Contribution

It introduces the concept of a dissipative current component in open quantum systems and provides an explicit expression for it within the Markov approximation.

Findings

Dissipative current component exists alongside Hamiltonian current.

Explicit formula for dissipative current derived under Markov approximation.

Numerical example demonstrates the role of dissipative current in a quantum system.

Abstract

We show that a dissipative current component is present in the dynamics generated by a Liouville-master equation, in addition to the usual component associated with Hamiltonian evolution. The dissipative component originates from coarse graining in time, implicit in a master equation, and needs to be included to preserve current continuity. We derive an explicit expression for the dissipative current in the context of the Markov approximation. Finally, we illustrate our approach 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 equation.