Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation

TL;DR

This paper derives a mathematically rigorous quantum master equation that includes nonsecular effects, preserves positivity, and adheres to thermodynamic principles, addressing a long-standing problem in open quantum systems.

Contribution

It provides a fully rigorous derivation of a nonsecular quantum master equation in the Gorini-Kossakowski-Lindblad-Sudarshan form, extending the weak-coupling limit.

Findings

Equation accounts for nearly degenerate energy levels.

Preserves positivity of the density operator.

Satisfies standard thermodynamic properties.

Abstract

Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini-Kossakowski-Lindblad-Sudarshan form (in particular, it preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The nonsecular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case.