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

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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. Skrypnyk^ab

^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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Applications to generalized Gaudin models, Bose--Hubbard dimers, and

Jaynes--Cummings--Dicke-type models

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Linking options:

https://www.mathnet.ru/eng/tmf9078

https://doi.org/10.4213/tmf9078

https://www.mathnet.ru/eng/tmf/v189/i1/p125

This publication is cited in the following 6 articles:

Agnieszka Wierzchucka, Francesco Piazza, Pieter W. Claeys, “Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models”, Phys. Rev. A, 109:3 (2024)
Paul A. Johnson, Advances in Quantum Chemistry, 2024
Alexandre Faribault, Claude Dimo, “'Bethe-ansatz-free' eigenstates for spin-1/2 Richardson–Gaudin integrable models”, J. Phys. A: Math. Theor., 55:41 (2022), 415205
P. W. Claeys, C. Dimo, S. De Baerdemacker, A. Faribault, “Integrable spin-1/2 Richardson Gaudin xyz models in an arbitrary magnetic field”, J. Phys. A-Math. Theor., 52:8 (2019), 08LT01
T. Skrypnyk, “Modified $n$ -level, $n-1$ -mode Tavis-Cummings model and algebraic Bethe ansatz”, J. Phys. A-Math. Theor., 51:1 (2018), 015204
Skrypnyk T., “Z _{2} -graded classical r -matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics”, J. Phys. A-Math. Theor., 49:36 (2016), 365201

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	326
Full-text PDF :	144
References:	71
First page:	24

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