Resonant transmission of fermionic carriers: comparison between solid-state physics and quantum optics approaches

TL;DR

This paper compares solid-state physics and quantum optics methods for describing resonant fermionic transmission, highlighting the regimes where each approach is most accurate, especially emphasizing the advantages of the non-Markovian master equation at high relaxation rates.

Contribution

It demonstrates the applicability of the non-Markovian master equation as an alternative to the Landauer-Büttiker approach for fermionic transport, identifying their respective validity regions.

Findings

Non-Markovian master equation accurately describes fermionic transmission at large relaxation rates.

Validity regions of both approaches are mapped in the system parameter space.

The non-Markovian approach surpasses the Landauer-Büttiker method in certain regimes.

Abstract

We revisit the phenomenon of the resonant transmission of fermionic carriers through a quantum device connected to two contacts with different chemical potentials. We show that, besides the traditional in solid-state physics Landauer-B\"uttiker approach, this phenomenon can be also described by the non-Markovian master equation for the reduced density matrix of the fermions in the quantum device. We identify validity regions of both approaches in the system parameter space and argue that for large relaxation rates the accuracy of the latter approach greatly exceeds the accuracy of the former.