Abstract

When simulating diffusion of a classical particle coupled to an environment, we don’t usually care about the exact state of the environment. Instead, we use a stochastic force to represent the interactions between the particle and it’s surroundings. This force is characterized by a correlation function that captures the essential statistical properties of the environment.

In this talk, we explore how to extend this idea to quantum systems. We introduce the concept of a “field operator” to represent the influence of a quantum environment on a system. Similar to the classical stochastic force, the field operator is characterized by its correlation functions, which encapsulate the statistical properties of the quantum environment.

We discuss how to calculate these correlation functions and how they can be used to simulate the dynamics of both a quantum and a classical system coupled to a quantum environment.