Extended Landauer-B\"{u}ttiker Formula for Current through Open Quantum Systems with Gain or Loss

TL;DR

This paper extends the Landauer-Büttiker formula to include gain and loss in open quantum systems, revealing novel effects like symmetry breaking, disorder-induced currents, and modified conductance laws.

Contribution

It introduces a generalized formula for current in systems with gain or loss using the Lindblad-Keldysh formalism, expanding transport theory in open quantum systems.

Findings

Gain and loss can generate current via symmetry breaking.

Disorder can induce current in systems with gain or loss.

Conductances remain continuous and obey Wiedemann-Franz law outside energy bands.

Abstract

The Landauer-B\"{u}ttiker formula, which characterizes the current flowing through a finite region connected to leads, has significantly advanced our understanding of transport. We extend this formula to describe particle and energy currents with gain or loss in the intermediate region by using the Lindblad-Keldysh formalism. Based on the derived formula, several novel effects induced by gain or loss in the current are discussed: the breaking of inversion symmetry in the gain and loss terms or in the system can lead to current generation; the anomalous phenomenon that disorder can induce current generation; the presence of gain and loss makes the thermal and electrical conductances continuous and ensures they follow the Wiedemann-Franz law even outside the energy band; the effect of bond loss-induced skin effect on current. This work deepens and extends our understanding of transport phenomena in open systems.