# Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach

## TL;DR

This paper introduces an iterative full counting statistics path integral (iFCSPI) method for accurately simulating heat exchange in open quantum systems, capturing strong coupling and non-Markovian effects.

## Contribution

The paper develops a numerically exact iFCSPI framework that extends influence functional path integrals to compute heat exchange cumulants in nonequilibrium quantum systems.

## Key findings

- Demonstrates the method's accuracy against perturbative approaches.
- Successfully computes steady-state heat currents and cumulants.
- Shows the method's capability to handle strong coupling and non-Markovian dynamics.

## Abstract

We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperature difference. Results are compared to perturbative treatments and demonstrate good agreement in the appropriate limits. The challenge of converging nonequilibrium quantities, currents and high order cumulants, is discussed in detail. The iFCSPI, a numerically exact technique, naturally captures strong system-bath coupling and non-Markovian effects of the environment. As such, it is a promising tool for probing fundamental questions in quantum transport and quantum thermodynamics.