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  • Open Access

Exact steady state of perturbed open quantum systems

Omar Nagib* and T. G. Walker

  • *Contact author: onagib@wisc.edu
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Phys. Rev. Research 7, 033076 – Published 18 July, 2025

DOI: https://doi.org/10.1103/kgsg-3npp

Abstract

We present a general nonperturbative 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 nontrivial 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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Phys. Rev. Research 7, 033076– Published 18 July, 2025
  • Received 20 January 2025
  • Accepted 24 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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