International Journal of Theoretical Physics

, Volume 57, Issue 6, pp 1888–1893 | Cite as

Time Evolution of the Wigner Operator as a Quasi-density Operator in Amplitude Dessipative Channel

  • Zhisong Yu
  • Guihua Ren
  • Ziyang Yu
  • Chenhuinan Wei
  • Hongyi Fan


For developing quantum mechanics theory in phase space, we explore how the Wigner operator \({\Delta } (\alpha ,\alpha ^{\ast } )\equiv \frac {1}{\pi } :e^{-2(\alpha ^{\ast } -\alpha ^{\dag })(\alpha -\alpha )}\):, when viewed as a quasi-density operator correponding to the Wigner quasiprobability distribution, evolves in a damping channel. with the damping constant κ. We derive that it evolves into
$$\frac{1}{T + 1}:\exp \frac{2}{T + 1}[-(\alpha^{\ast} e^{-\kappa t}-a^{\dag} )(\alpha e^{-\kappa t}-a)]: $$

where T ≡ 1 − e− 2κt. This in turn helps to directly obtain the final state ρ(t) out of the dessipative channel from the initial classical function corresponding to initial ρ(0). Throught the work, the method of integration within ordered product (IWOP) of operators is employed.


Wigner operator Quasi-density operator Amplitude dessipative channel IWOP method 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Zhisong Yu
    • 1
  • Guihua Ren
    • 2
  • Ziyang Yu
    • 3
  • Chenhuinan Wei
    • 3
  • Hongyi Fan
    • 4
  1. 1.College of Physics and Electronic ScienceHubei Normal UniversityHuangshiChina
  2. 2.College of Mechanic and Electric EngineeringHubei Polytechnic UniversityHuangshiChina
  3. 3.School of Physics and TechnologyWuhan UniversityWuhanChina
  4. 4.Department of Material Science and EngineeringUniversity of Science and Technology of ChinaHefeiChina

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