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

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.