×

zbMATH — the first resource for mathematics

Baxter \(Q\)-operators for the integrable discrete self-trapping chain. (English) Zbl 1178.82029
Theor. Math. Phys. 142, No. 2, 259-269 (2005); translation from Teor. Mat. Fiz. 142, No. 2, 310-321 (2005).
Summary: For the integrable discrete self-trapping chain, we construct Baxter \(Q\)-operators as the traces of the monodromy of certain \(M\)-operators that act in the quantum and auxiliary spaces. With this procedure, we obtain two basic \(M\)-operators and derive some functional relations between them such as intertwining relations and Wronskian-type relations between two basic \(Q\)-operators.

MSC:
82B23 Exactly solvable models; Bethe ansatz
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Yu. A. Izyumov and M. V. Medvedev, JETP, 21, 381-388 (1965); V. V. Gann and L. G. Zazunov, Fiz. Tverd. Tela, 15, 3535-3569 (1973); Y.-L. Wang and H. Callen, Phys. Rev., 160, 358-363 (1967); T. Oguchi and I. Ono, J. Phys. Soc. Japan, 26, 32-42 (1969); T. Wolfram and J. Callaway, Phys. Rev., 130, 2207-2217 (1963); I. Ono and Y. Endo, Phys. Rev. Lett. A, 41, 440-442 (1972).
[2] S. M. Tashpulatov, Theor. Math. Phys., 126, 403-408 (2001). · Zbl 0995.82019 · doi:10.1023/A:1010328203763
[3] E. Schrödinger, Proc. Roy. Irish. Acad. A, 48, 39-39 (1941). · Zbl 0063.06820
[4] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis, Acad. Press, New York (1972). · Zbl 0242.46001
[5] V. V. Val?kov, S. G. Ovchinnikov, and O. P. Petrakovskii, Fiz. Tverd. Tela, 30, 3044-3047 (1988).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.