Eigenvalues of the Liouvillians of Quantum Master Equation for a Harmonic Oscillator
arXiv:2006.04352 · doi:10.1016/j.physa.2020.124768
Abstract
The eigenvalues of the Liouvillians of Markovian master equation for a harmonic oscillator have a generic form. The Liouvillians considered are quadratic in the position coordinates or creation and annihilation operators, as well as having positive renormalized frequencies. We prove this by showing that a generic Liouvillian of this form can be similarly related to the Liouvillian of the Kossakowski--Lindblad equation, whose eigenvalues are already known. The left and right eigenfunctions of the generic Liouvillian also form a complete and biorthogonal set. Examples of similarly related right eigenfunctions are given.
arXiv commentTo appear in Physica A
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