Bethe Ansatz and Classical Hirota Equation
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 Smatrix itself are identified with a certain τfunctions 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 SineGordon equation. The paper is based on the recent study of classical integrable structures in quantum integrable systems.^{1}
 Publication:

International Journal of Modern Physics B
 Pub Date:
 1997
 DOI:
 10.1142/S0217979297000101
 arXiv:
 arXiv:condmat/9610132
 Bibcode:
 1997IJMPB..11...75W
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 15 pages, Latex, special World Scientific macros included