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arXiv · 2006.04352

Eigenvalues of the Liouvillians of Quantum Master Equation for a Harmonic Oscillator

B. A. Tay
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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.

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B. A. Tay. 2020-06-08. Eigenvalues of the Liouvillians of Quantum Master Equation for a Harmonic Oscillator. https://doi.org/10.1016/j.physa.2020.124768

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