Staying positive: going beyond Lindblad with perturbative master equations

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dc.creatorWhitney, Robert S.
dc.date2007-11-01
dc.date2008-03-26
dc.date.accessioned2026-07-07T09:32:25Z
dc.date.available2026-07-07T09:32:25Z
dc.descriptionThe perturbative master equation (Bloch-Redfield) is extensively used 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-Schon 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 analyze 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 show analytically that, once the time-dependence of the parameters is accounted for, positivity is preserved.
dc.description19 pages (4 figs). Extended discussion of earlier works. Appendix reviews derivation of Bloch-Redfield equation
dc.identifierhttps://arxiv.org/abs/0711.0074
dc.identifierhttp://arxiv.org/abs/0711.0074
dc.identifierJ. Phys. A: Math. Theor. 41, 175304 (2008)
dc.identifierdoi:10.1088/1751-8113/41/17/175304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158772
dc.subjectQuantum Physics
dc.subjectMesoscale and Nanoscale Physics
dc.titleStaying positive: going beyond Lindblad with perturbative master equations
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