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

Daigo Honda; Hiromichi Nakazato; Motoyuki Yoshida

doi:10.1063/1.3442363

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

Daigo Honda, Hiromichi Nakazato, Motoyuki Yoshida

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2 Citations (Scopus)

Abstract

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.

Original language	English
Article number	025006JMP
Journal	Journal of Mathematical Physics
Volume	51
Issue number	7
DOIs	https://doi.org/10.1063/1.3442363
Publication status	Published - 2010 Jul

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ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Cite this

Honda, D., Nakazato, H., & Yoshida, M. (2010). Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator. Journal of Mathematical Physics, 51(7), [025006JMP]. https://doi.org/10.1063/1.3442363

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10.1063/1.3442363