2007/11/30 by Robert S. Whitney · 3 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Spectroscopy and Quantum Chemical Studies #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/17/175304
published as J. Phys. A: Math. Theor. 41, 175304 (2008) · 19 pages (4 figs). Extended discussion of earlier works. Appendix reviews derivation of Bloch-Redfield equation
arxiv created 2008/03/26 · openalex publication_date 2008/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The perturbative master equation (Bloch–Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima–Zwanzig or Schoeller–Schön equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent . This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch–Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.