Matrix Model and Stationary Problem in Toda Chain

Details Matrix Model and Stationary Problem in Toda Chain Matrix Model and Stationary Problem in Toda Chain

2005-07-07

arxiv.org/abs/hep-th/0507071v1

Theor.Math.Phys. 146 (2006) 1-12; Teor.Mat.Fiz. 146 (2006) 3-16

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX; Based on talks at "Classical and quantum integrable systems", Dubna, January 2005 and "Selected topics of mod

Scientific paper

10.1007/s11232-006-0001-0

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.

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