On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations

Zhang, Yao-Zhong (2013) On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations. Journal of Mathematical Physics, 54 10: 102104.1-102104.13. doi:10.1063/1.4826356

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Author Zhang, Yao-Zhong
Title On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
Publication date 2013-10-01
Year available 2013
Sub-type Article (original research)
DOI 10.1063/1.4826356
Open Access Status File (Publisher version)
Volume 54
Issue 10
Start page 102104.1
End page 102104.13
Total pages 13
Place of publication College Park, MD United States
Publisher American Institute of Physics
Language eng
Subject 3109 Statistical and Nonlinear Physics
2610 Mathematical Physics
Abstract We study the solvability of the time-independent matrix Schrödinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model and its 2-photon and two-mode analogs are quasi-exactly solvable. We derive the exact, closed-form expressions for the energies and the allowed model parameters for all the three cases in the solvable subspaces. Up to a normalization factor, the eigenfunctions for these models are given by polynomials whose roots are determined by systems of algebraic equations.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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Citation counts: TR Web of Science Citation Count  Cited 21 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 12 times in Scopus Article | Citations
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Created: Fri, 29 Nov 2013, 07:15:41 EST by System User on behalf of School of Mathematics & Physics