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Open Quantum Systems Decoherence

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

arXiv
Authors: Daigo Honda, Hiromichi Nakazato, Motoyuki Yoshida

Year

2010

Paper ID

8957

Status

Preprint

Abstract Read

~2 min

Abstract Words

86

Citations

N/A

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.

Why This Paper Matters

  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
  • It adds a 2010 reference point for readers tracking recent quantum research.
  • A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1004.2044 [2] arXiv https://arxiv.org/abs/1004.2044 [3] Publisher https://arxiv.org/abs/1004.2044

Local Citation Graph (Related-Paper Links)

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