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Bethe Ansatz and Classical Hirota Equation | | P. Wiegmann
; | | Date: |
16 Oct 1996 | | Journal: | Int.J.Mod.Phys. B11 (1997) 75 | | Subject: | Statistical Mechanics; Quantum Algebra; Exactly Solvable and Integrable Systems | cond-mat.stat-mech hep-th math.QA nlin.SI q-alg solv-int | | Affiliation: | James Franck Institute; Enrico Fermi Institute of the University of Chicago; Landau Institute for Theoretical Physics | | Abstract: | We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up. Namely, the eigenvalues of the quantum transfer matrix and the scattering $S$-matrix itself are identified with a certain $ au$-functions of the discrete Liouville equation. The Bethe ansatz equations are obtained as dynamics of zeros. For comparison we also present the Bethe ansatz equations for elliptic solutions of the classical discrete Sine-Gordon equation. The paper is based on the recent study of classical integrable structures in quantum integrable systems, hep-th/9604080. | | Source: | arXiv, cond-mat/9610132 | | Services: | Forum | Review | PDF | Favorites | |
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