Comparative study for two-terminal transport through a lossy one-dimensional quantum wire

TL;DR

This paper analyzes two-terminal quantum transport in a lossy one-dimensional wire, revealing universal current formulas that connect with three-terminal systems and are applicable across quantum statistics.

Contribution

It provides an analytic framework for understanding lossy two-terminal transport using Dyson equations and Landauer-Büttiker formalism, bridging to three-terminal systems.

Findings

Derived analytic expressions for particle and energy currents in lossy systems.

Established the universality of current formulas across quantum statistics.

Connected two-terminal lossy transport to three-terminal non-lossy systems.

Abstract

Motivated by realization of the dissipative quantum point contact in ultracold atomic gases, we investigate a two-terminal mesoscopic transport system in which a single-particle loss is locally present in a one-dimensional chain. By means of the Dyson equation approach in the Keldysh formalism that can incorporate dissipative effects, we reveal analytic structures of the particle and energy currents whose formal expressions correspond to ones in certain three-terminal systems where the particle loss is absent. The obtained formulas are also consistent with non-hermitian and three-terminal Landauer-B\"{u}ttiiker analyses. The universality on the current expressions holds regardless of quantum statistics and may be useful for understanding lossy two-terminal transport in terms of three-terminal transport and vice versa.