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

TL;DR

This paper introduces a recursive perturbative method to construct time-convolutionless generators in a generalized Lindblad form for open quantum systems, enabling systematic analysis of non-Markovian dynamics and strong coupling effects.

Contribution

It presents a novel recursive approach to derive TCL generators at any order while maintaining a Lindblad-like structure, applicable to arbitrary open quantum systems.

Findings

Explicitly computed the generator up to fourth order.

Validated the method's effectiveness for non-Markovian and strong-coupling regimes.

Provided a canonical form that separates Hamiltonian and dissipative parts.

Abstract

We develop a recursive perturbative expansion for the time-convolutionless (TCL) 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.