Non-Markovian master equation for quantum transport of fermionic carriers

TL;DR

This paper introduces a simple model for quantum transport of fermionic carriers across a chain connecting reservoirs, deriving a master equation in both Markovian and non-Markovian regimes, revealing resonant transport phenomena.

Contribution

It provides a feasible model and analytical solutions for the master equation governing fermionic quantum transport, including non-Markovian effects.

Findings

Analytical solution of the Markovian master equation.

Reduction of the non-Markovian problem to an algebraic equation.

Resonant transport behavior similar to Landauer's conductance.

Abstract

We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix in a closed form in both Markov and Born approximations. In the Markov approximation the master equation is solved analytically, whereas in the Born approximation the problem is reduced to an algebraic equation for the single particle density matric in the Redfield form. The non-Markovian equation is shown to lead to resonant transport similar to Landauer's conductance.