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Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems

Alessandra Colla1,2,3,*, Heinz-Peter Breuer3,4, and Giulio Gasbarri5,6,†

  • *Contact author: alessandra.colla@unimi.it
  • †Contact author: giulio.gasbarri@uni-siegen.de
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Phys. Rev. A 112, 052222 – Published 24 November, 2025

DOI: https://doi.org/10.1103/9j8d-jxgd

Abstract

We develop a recursive perturbative expansion for the time-convolutionless generator of an open quantum system in a generalized Lindblad form. This formulation provides a systematic approach to derive the generator at arbitrary order while preserving a Lindblad-like structure, without imposing assumptions on the system or environment beyond an initially uncorrelated state. The generator is written, at all orders, in a canonical form, which also corresponds to the minimal dissipation condition, which uniquely specifies the decomposition of the generator into Hamiltonian and dissipative contributions. To validate the method and show its effectiveness in addressing non-Markovian dynamics and strong-coupling effects, we compute the generator explicitly up to fourth order.

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Phys. Rev. A 112, 052222– Published 24 November, 2025
  • Received 9 May 2025
  • Accepted 3 November 2025
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