A partition-free approach to transient and steady-state charge currents

TL;DR

This paper develops a partition-free method to analyze the evolution and stabilization of charge currents in mesoscopic Fermi systems, deriving a Landauer-type formula for the steady state.

Contribution

It introduces a novel partition-free approach to compute transient and steady-state currents in mesoscopic systems without initial partitioning.

Findings

Charge current stabilizes around a steady state value.

Steady state current is given by a Landauer-type formula.

Method applies to systems initially in grand canonical equilibrium.

Abstract

We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady state value, which is given by a Landauer-type formula.