Completely Positive Post-Markovian Master Equation via a Measurement Approach

Abstract

A new post-Markovian quantum master equation is derived, that includes bath memory effects via a phenomenologically introduced memory kernel k(t). The derivation uses as a formal tool a probabilistic single-shot bath-measurement process performed during the coupled system-bath evolution. The resulting analytically solvable master equation interpolates between the exact Nakajima-Zwanzig equation and the Markovian Lindblad equation. A necessary and sufficient condition for complete positivity in terms of properties of k(t) is presented, in addition to a prescription for the experimental determination of k(t). The formalism is illustrated with examples.

v2: 5 pages, incl. 1 figure. A more general post-Markovian master equation is derived as an intermediate step, and some steps in the derivation are clarified

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