# Statistics of heat transport across capacitively coupled double quantum dot circuit

## TL;DR

This paper investigates heat transport and fluctuations in a double quantum dot system, revealing how interactions and coupling influence heat current behavior and confirming fluctuation theorems through advanced theoretical methods.

## Contribution

It introduces a comprehensive analysis of heat fluctuations using Lindblad and Schwinger-Keldysh approaches, highlighting the effects of Coulomb interaction and system-reservoir coupling.

## Key findings

- Heat current and fluctuations are non-monotonic functions of interaction and coupling strength.
- Large Coulomb interaction and coupling suppress heat transport and fluctuations.
- Steady-state fluctuation theorem is verified for the quantum dot system.

## Abstract

We study heat current and the full statistics of heat fluctuations in a capacitively-coupled double quantum dot system. This work is motivated by recent theoretical studies and experimental works on heat currents in quantum dot circuits. As expected intuitively, within the (static) mean-field approximation, the system at steady-state decouples into two single-dot equilibrium systems with renormalized dot energies, leading to zero average heat flux and fluctuations. This reveals that dynamic correlations induced between electrons on the dots is solely responsible for the heat transport between the two reservoirs. To study heat current fluctuations, we compute steady-state cumulant generating function for heat exchanged between reservoirs using two approaches : Lindblad quantum master equation approach, which is valid for arbitrary coulomb interaction strength but weak system-reservoir coupling strength, and the saddle point approximation for Schwinger-Keldysh coherent state path integral, which is valid for arbitrary system-reservoir coupling strength but weak coulomb interaction strength. Using thus obtained generating functions, we verify steady-state fluctuation theorem for stochastic heat flux and study the average heat current and its fluctuations. We find that the heat current and its fluctuations change non-monotonically with the coulomb interaction strength ($U$) and system-reservoir coupling strength ($\Gamma$) and are suppressed for large values of $U$ and $\Gamma$.