Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Applications + Practical Conceptualization + Mathematics = fruitful InnovationAnalytical Solutions of Basic Models in Quantum Optics

Applications + Practical Conceptualization + Mathematics = fruitful Innovation: Analytical... [The recent progress in the analytical solution of models invented to describe theoretically the interaction of matter with light on an atomic scale is reviewed. The methods employ the classical theory of linear differential equations in the complex domain (Fuchsian equations). The linking concept is provided by the Bargmann Hilbert space of analytic functions, which is isomorphic to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2(\mathbb {R})$$\end{document}, the standard Hilbert space for a single continuous degree of freedom in quantum mechanics. I give the solution of the quantum Rabi model in some detail and sketch the solution of its generalization, the asymmetric Dicke model. Characteristic properties of the respective spectra are derived directly from the singularity structure of the corresponding system of differential equations.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Applications + Practical Conceptualization + Mathematics = fruitful InnovationAnalytical Solutions of Basic Models in Quantum Optics

Part of the Mathematics for Industry Book Series (volume 11)
Editors: Anderssen, Robert S.; Broadbridge, Philip; Fukumoto, Yasuhide; Kajiwara, Kenji; Takagi, Tsuyoshi; Verbitskiy, Evgeny; Wakayama, Masato

Loading next page...
 
/lp/springer-journals/applications-practical-conceptualization-mathematics-fruitful-B6jHJXLppc
Publisher
Springer Japan
Copyright
© Springer Japan 2016
ISBN
978-4-431-55341-0
Pages
75 –92
DOI
10.1007/978-4-431-55342-7_7
Publisher site
See Chapter on Publisher Site

Abstract

[The recent progress in the analytical solution of models invented to describe theoretically the interaction of matter with light on an atomic scale is reviewed. The methods employ the classical theory of linear differential equations in the complex domain (Fuchsian equations). The linking concept is provided by the Bargmann Hilbert space of analytic functions, which is isomorphic to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2(\mathbb {R})$$\end{document}, the standard Hilbert space for a single continuous degree of freedom in quantum mechanics. I give the solution of the quantum Rabi model in some detail and sketch the solution of its generalization, the asymmetric Dicke model. Characteristic properties of the respective spectra are derived directly from the singularity structure of the corresponding system of differential equations.]

Published: Sep 19, 2015

Keywords: Quantum optics; Bargmann space; Differential equations; Singularity theory; Integrable systems

There are no references for this article.