On the Redfield and Lindblad master equations

• URL: http://arxiv.org/abs/2602.13429v1
• Date: Fri, 13 Feb 2026 20:06:39 GMT
• Title: On the Redfield and Lindblad master equations
• Authors: Hans C. Fogedby,
• Abstract summary: We identify a discrepancy in the popular and standard Redfield equation.<n>The discrepancy is related to the diagrammatic expansion and a consistency requirement in the quasi-particle approximation.<n>We obtain formal equivalence between the energy-conserving Redfield equation and the Lindblad equation without invoking the rotating wave approximation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a previous work we developed a field theoretical approach to open quantum systems using condensed matter methods. In the Born approximation we derived the Redfield equation on the basis of a multi-oscillator bath, a Dyson equation, a diagrammatic expansion and a quasi-particle approximation. In addition applying a rotating wave approximation we obtained the Lindblad equation describing a proper quantum map. The issue regarding the additional rotating wave approximation was left as an open problem. The present work addresses the open problem and presents new results. We identify a discrepancy in the popular and standard Redfield equation. The discrepancy is associated with the well-known fact that the Redfield equation does not represent a proper quantum map. The discrepancy is related to the diagrammatic expansion and a consistency requirement in the quasi-particle approximation. The explicit resolution of this discrepancy is obtained by imposing energy conservation on the Born level. As a result we obtain formal equivalence between the energy-conserving Redfield equation and the Lindblad equation without invoking the rotating wave approximation. We provide a detailed mapping of the field theoretical approach to the standard microscopic derivation in the theory of open quantum systems.

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