Exact steady state of perturbed open quantum systems

TL;DR

This paper introduces a non-perturbative, exact method for determining the steady state of open quantum systems under various perturbations, significantly improving computational efficiency.

Contribution

The authors develop a novel approach using the Drazin inverse and diagonalization to exactly compute steady states and their dependence on perturbations in open quantum systems.

Findings

Achieves exact steady state calculations for complex quantum systems.

Provides a computational speedup of up to several orders of magnitude.

Enables analytic operations like differentiation and averaging on steady states.

Abstract

We present a general non-perturbative method to determine the exact steady state of open quantum systems under perturbation. The method works for systems with a unique steady state and the perturbation may be time-independent or periodic, and of arbitrarily large amplitude. Using the Drazin inverse and a single diagonalization, we construct an operator that generates the entire dependence of the steady state on the perturbation parameter. The approach also enables exact analytic operations-such as differentiation, integration, and ensemble averaging-with respect to the parameter, even when the steady state is computed numerically. We apply the method to three non-trivial open quantum systems, showing that it achieves exact results, with a computational speedup of one to several orders of magnitude for calculations requiring large sampling, compared to previous approaches.