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Symmetry of bilinear master equations for a quantum oscillator

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  • Tay, B.A.

Abstract

We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the probability of reduced dynamics should be adjoint-symmetric, and they are not limited to the pure product of unitary operators in the bra and ket space but could be a mixture of them. We need to include the more general transformation operators to explore the full symmetry of generic reduced dynamics. We discuss how the operators are related to those considered in previous works, and illustrate how they leave the reduced dynamics form invariant, or map one into the other. The positive semidefinite requirement on the density operator can be imposed to give a valid range of transformation parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:468:y:2017:i:c:p:578-589
    DOI: 10.1016/j.physa.2016.10.067
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    References listed on IDEAS

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    1. Petrosky, T. & Prigogine, I. & Tasaki, S., 1991. "Quantum theory of non-integrable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 173(1), pages 175-242.
    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.
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    Cited by:

    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).
    2. 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.

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