Limited validity of the Kubo formula for thermal conduction in modular quantum systems

TL;DR

This paper investigates the applicability of the Kubo formula for thermal conduction in modular quantum systems, highlighting its limitations and validating results through numerical simulations and direct Schrödinger equation solutions.

Contribution

It critically assesses the validity of the Kubo formula for heat conduction in modular quantum systems and compares theoretical predictions with numerical data.

Findings

Kubo formula has limited validity for thermal conduction in modular systems

Numerical evaluations show discrepancies with direct Schrödinger solutions

The applicability depends on system specifics and coupling strength

Abstract

The Kubo formula describes a current as a response to an external field. In the case of heat conduction there is no such external field. We analyze why and to what extend it is nevertheless justified to describe heat conduction in modular quantum systems by the Kubo formula. Modular we call systems that may be described as consisting of weakly coupled identical subsystems. We explain in what sense this description applies to a large class of systems. Furthermore, we numerically evaluate the Kubo formula for some finite modular systems. We compare the results with data obtained from the direct numerical solution of the corresponding time-dependent Schroedinger equation.