Matrix Model and Stationary Problem in Toda Chain
High Energy Physics - Theory
2009-11-11 v1
Abstract
We analyze the stationary problem for the Toda chain, and show that arising geometric data exactly correspond to the multi-support solutions of one-matrix model with a polynomial potential. For the first nontrivial examples the Hamiltonians and symplectic forms are calculated explicitly, and the consistency checks are performed. The corresponding quantum problem is formulated and some its properties and perspectives are discussed.
Keywords
Cite
@article{arxiv.hep-th/0507071,
title = {Matrix Model and Stationary Problem in Toda Chain},
author = {A. Marshakov},
journal= {arXiv preprint arXiv:hep-th/0507071},
year = {2009}
}
Comments
11 pages, LaTeX; Based on talks at "Classical and quantum integrable systems", Dubna, January 2005 and "Selected topics of modern mathematical physics", St.Petersburg, June 2005, and a lecture for the minicourse: "Toda lattices: basics and perspectives", Fields Institute, Toronto, April 2005