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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Bethe ansatz for the deformed Gaudin model; pp. 326–331

(Full article in PDF format) doi: 10.3176/proc.2010.4.11


Authors

Petr Kulish, Nenad Manojlović, Maxim Samsonov, Alexander Stolin

Abstract

A deformation of the sl(2) Gaudin model by a Jordanian r-matrix depending on the spectral parameter is constructed. The energy spectrum is preserved and recurrent creation operators are proposed.

Keywords

Gaudin models, algebraic Bethe ansatz.

References

  1. Gaudin , M. La fonction d’onde de Bethe. Masson , Paris , 1983.

  2. Sklyanin , E. K. Separation of variables in the Gaudin model. J. Soviet. Math. , 1989 , 47 , 2473–2488.
doi:10.1007/BF01840429

  3. Kulish , P. P. and Sklyanin , E. K. Solution of the Yang–Baxter equation. J. Soviet. Math. , 1982 , 19 , 1596–1620.
doi:10.1007/BF01091463

  4. Kulish , P. P. and Stolin , A. A. Deformed Yangians and integrable models. Czech. J. Phys. , 1997 , 47 , 1207–1212.
doi:10.1023/A:1022869414679

  5. Kulish , P. P. Twisted sl(2) Gaudin model. PDMI preprint , 2002 , 08/2002.

  6. Manojlović , N. and António , N. C. sl2 Gaudin model with Jordanian twist. J. Math. Phys. , 2005 , 46 , 102701 , 19 pp.

  7. Stolin , A. A. On rational solutions of Yang–Baxter equation for sl(n). Math. Scand. , 1991 , 69 , 57–80.

  8. Stolin , A. A. Constant solutions of Yang–Baxter equation for sl(2) and sl(3). Math. Scand. , 1991 , 69 , 81–88.

  9. Sklyanin , E. K. , Takhtajan , L. A. , and Faddeev , L. D. Quantum inverse problem method. Teoret. Mat. Fiz. , 1979 , 40 , 194–220.

10. Khoroshkin , S. M. , Stolin , A. A. , and Tolstoy , V. N. Deformation of Yangian Y(sl2). Comm. Algebra , 1998 , 26 , 1041–1055.
doi:10.1080/00927879808826182

11. Khoroshkin , S. M. , Stolin , A. A. , and Tolstoy , V. N. q-power function over q-commuting variables and deformed XXX and XXZ chains. Phys. Atomic Nuclei , 1979 , 64 , 2173–2178.
doi:10.1134/1.1432921
 
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Current Issue: Vol. 67, Issue 4 in Press, 2018




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