Quantum Heat Transport: Perturbation Theory in Liouville Space

TL;DR

This paper introduces a perturbation theory approach in Liouville space to analyze quantum heat transport in chains of subsystems coupled to heat baths, enabling calculation of heat current, temperature profiles, and conductivity.

Contribution

It develops a novel method extending Kubo techniques to Liouville space for quantum heat transport analysis.

Findings

Method effectively computes heat current and temperature profiles.

Applicable to various types of next neighbor interactions.

Provides a framework for analyzing quantum heat conductivity.

Abstract

We consider chains consisting of several identical subsystems weakly coupled by various types of next neighbor interactions. At both ends the chain is coupled to a respective heat bath with different temperature modeled by a Lindblad formalism. The temperature gradient introduced by this environment is then treated as an external perturbation. We propose a method to calculate the heat current and the local temperature profile of the resulting stationary state as well as the heat conductivity in such systems. This method is similar to Kubo techniques used e.g. for electrical transport but extended here to the Liouville space.