Heat conductivity in small quantum systems: Kubo formula in Liouville space

TL;DR

This paper develops a method to evaluate heat conductivity in small quantum chains by extending Kubo techniques to Liouville space, considering heat baths modeled by Lindblad formalism and treating temperature gradients as perturbations.

Contribution

It introduces a novel approach to compute heat current and temperature profiles in quantum systems using Liouville space extension of Kubo formulas.

Findings

Method successfully evaluates heat current and temperature profiles.

Applicable to systems with weakly coupled subsystems and Lindblad baths.

Provides a framework for analyzing quantum heat transport.

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 evaluate 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.