2010/04/30 by Daigo Honda, Hiromichi Nakazato, Motoyuki Yoshida · 1 citation
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.3442363
published as J. Math. Phys. 51, 072107 (2010) · 22pages, no figure; title changed, minor corrections, references added; minor corrections
openalex publication_date 2010/07/01 · arxiv created 2010/07/29 · arxiv updated 2010/07/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.