# Spectral representation of the heat current in a driven Josephson junction

## TL;DR

This paper presents a spectral method to analyze heat transport in driven Josephson junctions, distinguishing dissipative and reactive components, with implications for designing advanced cooling devices.

## Contribution

It introduces a spectral representation of heat current in driven Josephson junctions, clarifying reactive versus dissipative contributions and their physical interpretation.

## Key findings

- Reactive heat current is identified as non-contributing to long-term averages.
- Spectral representation simplifies analysis of heat exchange in driven Josephson systems.
- Potential applications in developing new cooling technologies.

## Abstract

We discuss thermal transport through a Josephson junction in a time-dependent situation. We write the spectral representation of the heat current pumped by a generic drive. This enables separation of the dissipative and reactive contributions, of which the latter do not contribute to long-time averages. We discuss the physical interpretation, and note that the condensate heat current identified in [K. Maki and A. Griffin, Phys. Rev. Lett. 15, 921 (1965)] is purely reactive. The results enable a convenient description of heat exchanges in a Josephson system in the presence of an external drive, with possible applications for the implementation of new cooling devices.