  The 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.
