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

• URL: http://arxiv.org/abs/2006.04352v1
• Date: Mon, 8 Jun 2020 04:59:22 GMT
• Title: Eigenvalues of the Liouvillians of Quantum Master Equation for a Harmonic Oscillator
• Authors: B. A. Tay
• Abstract summary: We prove that a generic Liouvillian of this form can be similarly related to the Liouvillian of the Kossakowski--Lindblad equation. The left and right eigenfunctions of the generic Liouvillian also form a complete and biorthogonal set.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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