Eigenvalues of the Liouvillians of quantum master equation for a harmonic oscillator

B.A. Tay

Physica A: Statistical Mechanics and its Applications, 2020, vol. 556, issue C

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.

Keywords: Spectral analysis; Harmonic oscillator; Liouville operator; Quantum master equation; Open quantum systems (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:556:y:2020:i:c:s0378437120303885

DOI: 10.1016/j.physa.2020.124768

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