Time-Loop Formalism for Irreversible Quantum Problems: Steady State Transport in Junctions with Asymmetric Dynamics

Non-unitary quantum mechanics has been used in the past to study irreversibility, dissipation and decay in a variety of physical systems. In this letter, we propose a general scheme to deal with systems governed by non-Hermitian Hamiltonians. We argue that the Schwinger-Keldysh formalism gives a natural description for those problems. To elucidate the method, we study a simple model inspired by mesoscopic physics --an asymmetric junction. The system is governed by a non-Hermitian Hamiltonian which captures essential aspects of irreversibility.