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 $\to$ Toda reductions, Nuclear Physics B 529:3 (1998) 547-566 doi

P. Deift, L. C. Li, T. Nanda, C. Tomei, The Toda flow on a generic orbit is integrable, Commun. Pure Appl. Math. 39:2 (1986) 183–232 (doi; with short earlier announcement with the same title in Bull. Amer. Math. Soc. 11:2 (1988) 367–368)

Last revised on July 31, 2024 at 08:31:11.
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