# Accessing the bath information in open quantum systems with the stochastic c-number Langevin equation method

## TL;DR

This paper introduces a stochastic c-number Langevin equation method that enables direct access to bath information in open quantum systems, providing a more comprehensive understanding of system-bath interactions.

## Contribution

The work develops a novel stochastic approach that allows simultaneous analysis of system and bath dynamics, extending traditional methods that only focus on the system.

## Key findings

- Successfully applied to models like pure dephasing and spin-boson.
- Able to extract bath information alongside system dynamics.
- Demonstrated effectiveness in quantum dot-phonon interactions.

## Abstract

In traditional open quantum systems, the baths are usually traced out so that only the system information is left in the equations of motion. However, recent studies reveal that using only the system degrees of freedom can be insufficient. In this work, we develop a stochastic c-number Langevin equation method which can conveniently access the bath information. In our method, the studied quantities are the expectation values of operators which can contain both system operators and bath operators. The dynamics of the operators of interest is formally divided into separate system and bath parts, with auxiliary stochastic fields. After solving the independent stochastic dynamics of the system part and the bath part, we can recombine them by taking the average over these stochastic fields to obtain the desired quantities. Several applications of the theory are highlighted, including the pure dephasing model, the spin-boson model, and an optically excited quantum dot coupled to a bath of phonons.