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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 1, Pages 125–146
DOI: https://doi.org/10.4213/tmf9078 (Mi tmf9078) 		 
This article is cited in 6 scientific papers (total in 6 papers)

“Twisted” rational $r$-matrices and the algebraic Bethe ansatz: Applications to generalized Gaudin models, Bose–Hubbard dimers, and Jaynes–Cummings–Dicke-type models

T. V. Skrypnykab

a Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
b University of Milano-Bicocca, Milano, Italy
Full-text PDF (521 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf9078
Abstract: We construct quantum integrable systems associated with the Lie algebra $gl(n)$ and non-skew-symmetric "shifted and twisted" rational $r$-matrices. The obtained models include Gaudin-type models with and without an external magnetic field, $n$-level $(n-1)$-mode Jaynes–Cummings–Dicke-type models in the $\Lambda$-configuration, a vector generalization of Bose–Hubbard dimers, etc. We diagonalize quantum Hamiltonians of the constructed integrable models using a nested Bethe ansatz.
Keywords: integrable system, classical $r$-matrix, algebraic Bethe ansatz.
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 1, Pages 1509–1527
DOI: https://doi.org/10.1134/S004057791610010X
Bibliographic databases:
MSC: 17B80, 81R12, 82B23
Language: Russian
Citation: T. V. Skrypnyk, ““Twisted” rational $r$-matrices and the algebraic Bethe ansatz: Applications to generalized Gaudin models, Bose–Hubbard dimers, and Jaynes–Cummings–Dicke-type models”, TMF, 189:1 (2016), 125–146; Theoret. and Math. Phys., 189:1 (2016), 1509–1527
Citation in format AMSBIB
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\paper ``Twisted'' rational $r$-matrices and the algebraic Bethe ansatz:
Applications to generalized Gaudin models, Bose--Hubbard dimers, and
Jaynes--Cummings--Dicke-type models
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\pages 125--146
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:52
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