Separation of Variables in Integrable Systems

Supervisor

Dr. Vladimir Mangazeev Phone: 6125 2952

A separation of variables (SoV) originally appeared in the classical papers of 19th century scientists. During last decades it was recognized that, properly generalized, this method can be the most universal approach in the analysis of dynamics in integrable systems. One of the challenging problems is to apply SoV to a dynamical system of relativistic one-dimensional particles with a special interaction (trigonometric Ruijsenaars model). This model has deep connections with both physics and mathematics. From one side it describes the system of particles with fractional statistics. From another side its eigenfunctions are given by Macdonald symmetric polynomials in many variables. In this project the properties of this system will be studied via a reduction to a set of dynamical systems in one variable