Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 41, Issue 17, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/41/17/175304
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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-Schron 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.
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