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Keywords:

  • Non-Hermitian;
  • non-equilibrium;
  • quantum transport;
  • quantum dots;
  • open quantum systems.

Abstract

We present two classic case studies of non-equilibrium transport from the mesoscopics literature, – a single-channel tunneling junction and a tunneling junction with an embedded resonant level –, that we generalized to the non-Hermitian case. We use these problems to illustrate the characteristics of the non-linear transport due to the asymmetric dynamics inherent of the non-Hermitian problem. We employ a generalized time-loop Green's function formalism that was developed explicitly to define and deal with these problems, and that constitutes a powerful and general tool for this type of studies. We point out important differences with the standard Hermitian case.