Toda lattice is a particular completely integrable system, a model of a 1-dimensional crystal. It can be generalized to general root systems. Integrability of Toda lattice has been shown in Flashka 1974 using an interpretation as a flow on the space of symmetric tridiagonal matrices.
Relation to other models
Toda lattice can be obtained by reduction from Wess-Zumino models.
Morikazu Toda, Vibration of a chain with a non-linear interaction“, J. Phys. Soc. Jpn., 22 (2) (1967) 431-436 doi
Hermann Flashka, The Toda lattice, II. Existence of integrals, Phys. Rev. B 9 (1974) 1924 doi
J. Moser, Three integrable Hamiltonian systems connected with isospectral deformations, Surveys in Applied Mathematics, Essays Dedicated to S.M. Ulam, 1976, 235–258 doi
Bertram Kostant, The solution to a generalized Toda lattice and representation theory, Adv. Math. 34, 195–338 (1998) pdf
L. O’Raifeartaigh, V. V. Sreedhar, Path integral formulation of the conformal Wess-Zumino-Witten Toda reductions, Nuclear Physics B 529:3 (1998) 547-566 doi
Last revised on July 7, 2024 at 14:59:21.
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