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Making non-Markovian master equations accessible with approximate environments

Gerardo Suárez* and Michał Horodecki

  • International Centre for Theory of Quantum Technologies, University of Gdansk, 80-308 Gdansk, Poland

  • *Contact author: gerardo.suarez@phdstud.ug.edu.pl
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Phys. Rev. E 113, 064121 – Published 9 June, 2026

DOI: https://doi.org/10.1103/kcff-b5mr

Abstract

Accurate and efficient simulation of open quantum systems remains a significant challenge, particularly for non-Markovian dynamics. We demonstrate the profound utility of expressing the environmental correlation function as a sum of damped sinusoidals within master equations. While not strictly required, this decomposition offers substantial benefits, crucially reducing the cost of Lamb-shift and decay-rate calculations without sacrificing accuracy. Furthermore, this approach enables straightforward calculation of Lamb-shift corrections, bypassing the need for complex principal value integration. We show that these Lamb-shift effects are demonstrably non-negligible in heat transport scenarios and are needed for an accurate description. Unlike in the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation, the noncommuting nature of the Lamb shift with the Hamiltonian in non-Markovian descriptions, coupled with GKLS's inaccuracies at early times, brings the necessity of non-Markovian descriptions for finite-time thermodynamics. In the weak-coupling regime, our master equation formulations with exponential decomposition achieve accuracy comparable to numerically exact methods. This methodology significantly simplifies and accelerates the simulation of non-Markovian dynamics in open quantum systems, offering a more reliable and computationally tractable alternative akin to a global master equation.

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Corrections

21 August, 2026

Correction: The statement acknowledging that Table I was adapted from another work was missing from the caption and has been added.

Article Text

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Phys. Rev. E 113, 064121– Published 9 June, 2026
  • Received 18 July 2025
  • Revised 8 October 2025
  • Accepted 18 May 2026
  • Corrected 21 August 2026
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