Symmetry of bilinear master equations for a quantum oscillator

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.

arXiv commentTypos in Eq.(14) are corrected

References in corpus (6)

• Concepts and methods in the theory of open quantum systems
• Exact time evolution and master equations for the damped harmonic oscillator
• Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
• On the Thermal Symmetry of the Markovian Master Equation
• Star-unitary transformations. From dynamics to irreversibility and stochastic behavior
• Exact Markovian kinetic equation for a quantum Brownian oscillator

Cited by in corpus (6)

• Eigenvalues of the Liouvillians of Quantum Master Equation for a Harmonic Oscillator
• Damping modes of harmonic oscillator in open quantum systems
• Liouvillian exceptional points in continuous variable system
• Solutions of generic bilinear master equations for a quantum oscillator -- positive and factorized conditions on stationary states
• General symmetry in the reduced dynamics of two-level system
• Evolution of Gaussian mixed states under the Markovian master equation for a driven quantum oscillator