# Damping Law of Classical Weyl Correspondence of Density Operator in Amplitude Dessipative Channel

Ontology type: schema:ScholarlyArticle

### Article Info

DATE

2017-08-24

AUTHORS ABSTRACT

For developing quantum mechanics theory in phase space, we expolre how does an initial density operator ρ0’s classical Weyl correspondence function h0 evolve into ht in a damping channel. We derive the following integration transformation that relating them htα,α∗=2T∫d2βπh0β,β∗exp−2Tα∗−β∗e−κtα−βe−κt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$h_{t}\left (\alpha ,\alpha ^{\ast } \right ) =\frac {2}{T}\int \frac {d^{2}\beta } {\pi } h_{0}\left (\beta ,\beta ^{\ast } \right ) \exp \left [ -\frac {2}{T} \left (\alpha ^{\ast } -\beta ^{\ast } e^{-\kappa t}\right ) \left (\alpha -\beta e^{-\kappa t}\right ) \right ]$\end{document} this is the damping law of classical Weyl correspondence of density operator in amplitude dessipative channel. The integration method within Weyl ordered product of operators and Wigner operator’s Wel ordering form Δα,α∗=12::δα∗−a‡α−a::\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\Delta } \left (\alpha ,\alpha ^{\ast } \right ) =\frac {1}{2}{{\begin {array}{l}:\\:\end {array}}}\delta \left (\alpha ^{\ast } -a^{\dag } \right ) \left (\alpha -a\right ){{\begin {array}{l}:\\:\end {array}}}$\end{document} is essential to our derivation. More... »

PAGES

3534-3542

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10773-017-3518-0

DOI

http://dx.doi.org/10.1007/s10773-017-3518-0

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https://app.dimensions.ai/details/publication/pub.1091338344

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