# Thermal power of heat flow through a qubit

## TL;DR

This paper investigates the thermal power of heat flow through a qubit coupled to two thermal baths, deriving expressions for power in different interaction regimes using the spin-boson model.

## Contribution

It introduces a method to compute thermal power in a qubit-bath system using the NIBA approximation and the polaron picture, connecting correlation functions to heat flow.

## Key findings

- Derived expressions for thermal power in the weak interaction limit.
- Connected thermal power to bath correlation functions and energy splitting.
- Recovered known results in the weak coupling regime.

## Abstract

In this paper we consider thermal power of a heat flow through a qubit between two baths. The baths are modeled as set of harmonic oscillators initially at equilibrium, at two temperatures. Heat is defined as the change of energy of the cold bath, and thermal power is defined as expected heat per unit time, in the long-time limit. The qubit and the baths interact as in the spin-boson model, i.e. through qubit operator $\sigma_z$. We compute thermal power in an approximation analogous to `non-interacting blip' (NIBA) and express it in the polaron picture as products of correlation functions of the two baths, and a time derivative of a correlation function of the cold bath. In the limit of weak interaction we recover known results in terms of a sum of correlation functions of the two baths, a correlation functions of the cold bath only, and the energy split.