Integrable systems whose spectral curve is the graph of a function

Kanehisa Takasaki

Integrable systems whose spectral curve is the graph of a function

Exactly Solvable and Integrable Systems 2007-05-23 v3 High Energy Physics - Theory Mathematical Physics math.MP

Authors: Kanehisa Takasaki

Abstract

For some integrable systems, such as the open Toda molecule, the spectral curve of the Lax representation becomes the graph $C = \{(\lambda,z) \mid z = A(\lambda)\}$ of a function $A(\lambda)$ . Those integrable systems provide an interesting ``toy model'' of separation of variables. Examples of this type of integrable systems are presented along with generalizations for which $A(\lambda)$ lives on a cylinder, a torus or a Riemann surface of higher genus.

Keywords

integrable systems toda lattice positive maps in quantum information

Cite

@article{arxiv.nlin/0211021,
  title  = {Integrable systems whose spectral curve is the graph of a function},
  author = {Kanehisa Takasaki},
  journal= {arXiv preprint arXiv:nlin/0211021},
  year   = {2007}
}

Comments

latex2e, 15 pages, no figure; (v2) typos in eq. (25) etc. are corrected; (v3) a few typos are corrected. This article will be published in CRM Proceedings and Lecture Notes vol. 37

Integrable systems whose spectral curve is the graph of a function

Abstract

Keywords

Cite

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