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

Daigo Honda, Hiromichi Nakazato, Motoyuki Yoshida

Research output: Contribution to journalArticle

5 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 languageEnglish
Article number025006JMP
JournalJournal of Mathematical Physics
Volume51
Issue number7
DOIs
Publication statusPublished - 2010 Jul 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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