Finite representations of continuum environments

TL;DR

This paper introduces a new method for creating finite, sparse representations of quantum environments based on frequency influence, enabling more efficient simulations of open quantum systems.

Contribution

A novel framework for finite environment representations that simplifies high-frequency components, reducing computational costs in quantum system simulations.

Findings

Sparse high-frequency environment representation achieves significant speedup.

Constant influence of low-frequency modes on system dynamics.

Applicable to general open quantum system models.

Abstract

Understanding dissipative and decohering processes is fundamental to the study of quantum systems. An accurate and generic method for investigating these processes is to simulate both the system and environment, which, however, is computationally very demanding. We develop a novel approach to constructing finite representations of the environment based on the influence of different frequency scales on the system's dynamics. As an illustration, we analyze a solvable model of an optical mode decaying into a reservoir. The influence of the environment modes is constant for small frequencies, but drops off rapidly for large frequencies, allowing for a very sparse representation at high frequencies that gives a significant computational speedup in simulating the environment. This approach provides a general framework for simulating open quantum systems.