Kubo formula for finite size systems

TL;DR

This paper derives a Kubo-type formula for heat transport in finite-size systems, emphasizing the importance of including lead/bath coupling to avoid singularities and obtain accurate linear response calculations.

Contribution

It introduces a modified Kubo formula explicitly accounting for system-bath coupling, improving the accuracy of linear response calculations in finite systems.

Findings

Proper inclusion of bath coupling yields well-behaved heat response.

Avoids singularities from degenerate states common in infinite-system formulas.

Provides a practical method for finite-size thermal transport analysis.

Abstract

We demonstrate that the proper calculation of the linear response for finite-size systems can only be performed if the coupling to the leads/baths is explicitly taken into consideration. We exemplify this by obtaining a Kubo-type formula for heat transport in a finite-size system coupled to two thermal baths, kept at different temperatures. We show that the proper calculation results in a well-behaved response, without the singular contributions from degenerate states encountered when Kubo formulae for infinite-size systems are inappropriately used for finite-size systems.