Solutions of generic bilinear master equations for a quantum oscillator—Positive and factorized conditions on stationary states

B.A. Tay

Physica A: Statistical Mechanics and its Applications, 2017, vol. 477, issue C, 42-64

Abstract: We obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the Gaussian form. The well-behavedness and positive semidefiniteness of the stationary states could be characterized by a three-dimensional Minkowski vector. By requiring the stationary states to satisfy a factorized condition, we obtain a generic class of master equations that includes the well-known ones and their generalizations, some of which are completely positive. A further subset of the master equations with the Gibbs states as stationary states is also obtained. For master equations with not completely positive generators, an analysis on the stationary states for a given initial state suggests conditions on the coefficients of the master equations that generate positive evolution.

Keywords: Master equation; Damped oscillator; Open quantum systems; Positivity; Solutions (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:477:y:2017:i:c:p:42-64

DOI: 10.1016/j.physa.2017.02.020

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