Affine Toda-Sutherland Systems

Details Affine Toda-Sutherland Systems Affine Toda-Sutherland Systems

2003-09-08

arxiv.org/abs/hep-th/0309077v1

J.Phys.A37:1665-1680,2004

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e 22 pages with amsfonts and graphicx, 5 eps figures

Scientific paper

10.1088/0305-4470/37/5/013

A cross between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system, is introduced for any affine root system. Though it is not completely integrable but partially integrable, or quasi exactly solvable, it inherits many remarkable properties from the parents. The equilibrium position is algebraic, i.e. proportional to the Weyl vector. The frequencies of small oscillations near equilibrium are proportional to the affine Toda masses, which are essential ingredients of the exact factorisable S-matrices of affine Toda field theories. Some lower lying frequencies are integer times a coupling constant for which the corresponding exact quantum eigenvalues and eigenfunctions are obtained. An affine Toda-Calogero system, with a corresponding rational potential, is also discussed.

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