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 | |
| Publication status | Published - 2010 Jul 1 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Fingerprint Dive into the research topics of 'Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator'. Together they form a unique fingerprint.
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