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

Daigo Honda, Hiromichi Nakazato, Motoyuki Yoshida

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    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 languageEnglish
    Article number025006JMP
    JournalJournal of Mathematical Physics
    Issue number7
    Publication statusPublished - 2010 Jul


    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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