TY - JOUR
T1 - Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator
AU - Honda, Daigo
AU - Nakazato, Hiromichi
AU - Yoshida, Motoyuki
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2010/7
Y1 - 2010/7
N2 - 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.
AB - 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.
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U2 - 10.1063/1.3442363
DO - 10.1063/1.3442363
M3 - Article
AN - SCOPUS:77955540424
VL - 51
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 7
M1 - 025006JMP
ER -