Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator

Details Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator

2010-04-12

arxiv.org/abs/1004.2044v3

J. Math. Phys. 51, 072107 (2010)

Physics

Quantum Physics

22pages, no figure; title changed, minor corrections, references added; minor corrections

Scientific paper

10.1063/1.3442363

A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved. The solution yields the spectral resolution of the Liouvillian, that is, all eigenvalues and eigenprojections are obtained. This spectral resolution is discussed in depth in the context of the biorthogonal system and the rigged Hilbert space, and the contribution of each eigenprojection to expectation values of physical quantities is revealed. We also construct the ladder operators of the Liouvillian, which clarify the structure of the spectral resolution.

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