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

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  • Tay, B.A.

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.

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  • Tay, B.A., 2017. "Solutions of generic bilinear master equations for a quantum oscillator—Positive and factorized conditions on stationary states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 42-64.
    • Handle: RePEc:eee:phsmap:v:477:y:2017:i:c:p:42-64
    DOI: 10.1016/j.physa.2017.02.020
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    References listed on IDEAS

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    1. Tameshtit, Allan, 2013. "On the standard quantum Brownian equation and an associated class of non-autonomous master equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(3), pages 427-443.
    2. Caldeira, A.O. & Leggett, A.J., 1983. "Path integral approach to quantum Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(3), pages 587-616.
    3. Tay, B.A., 2017. "Symmetry of bilinear master equations for a quantum oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 578-589.
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    1. Tay, B.A., 2020. "Eigenvalues of the Liouvillians of quantum master equation for a harmonic oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).

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