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arXiv · 2501.06134

Exact steady state of perturbed open quantum systems

Omar Nagib·Thad G. Walker
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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.

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Omar Nagib, Thad G. Walker. 2025-01-10. Exact steady state of perturbed open quantum systems. https://doi.org/10.1103/kgsg-3npp

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