Dissipative Transport: Thermal Contacts and Tunnelling Junctions

TL;DR

This paper reviews and extends the theory of quantum transport between reservoirs, focusing on thermoelectric effects, entropy production, and currents, with explicit calculations demonstrating positivity and convergence of the series involved.

Contribution

It introduces a microscopic framework for quantum thermoelectric transport, providing explicit calculations and proving positivity of key quantities under certain conditions.

Findings

Explicit formulas for energy and particle currents

Proof of positivity of entropy production and resistance

Convergence of perturbation series under specific assumptions

Abstract

The general theory of simple transport processes between quantum mechanical reservoirs is reviewed and extended. We focus on thermoelectric phenomena, involving exchange of energy and particles. Entropy production and Onsager relations are relevant thermodynamic notions which are shown to emerge from the microscopic description. The theory is illustrated on the example of two reservoirs of free fermions coupled through a local interaction. We construct a stationary state and determine energy- and particle currents with the help of a convergent perturbation series. We explicitly calculate several interesting quantities to lowest order, such as the entropy production, the resistance, and the heat conductivity. Convergence of the perturbation series allows us to prove that they are strictly positive under suitable assumptions on the interaction between the reservoirs.