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

Daigo Honda; Hiromichi Nakazato; Motoyuki Yoshida

doi:10.1063/1.3442363

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

Daigo Honda, Hiromichi Nakazato, Motoyuki Yoshida

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Article number	025006JMP
Journal	Journal of Mathematical Physics
Volume	51
Issue number	7
DOIs	https://doi.org/10.1063/1.3442363
Publication status	Published - 2010 Jul 1

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1063/1.3442363

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

@article{5a431581b8a74ca2b9b87b65ae29bba0,

title = "Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator",

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.",

author = "Daigo Honda and Hiromichi Nakazato and Motoyuki Yoshida",

year = "2010",

month = jul,

day = "1",

doi = "10.1063/1.3442363",

language = "English",

volume = "51",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics Publising LLC",

number = "7",

}

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

PY - 2010/7/1

Y1 - 2010/7/1

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.

UR - http://www.scopus.com/inward/record.url?scp=77955540424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955540424&partnerID=8YFLogxK

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 -