On a Duality in Calogero-Moser-Sutherland Systems

Abstract

We point out a map between the dynamics of a non-relativistic system of $N$ particles in one dimension interacting via the pair-wise potentials $U_I(q)=({\nu }^2/4R^2){\sin }^2(q/2R)$ and the one of the particles with the pair potential $U_{II}(q)={\nu }^2/q^2$ and the external potential $U_{ext}={\omega }^2{q}^2/2$. The natural relation between the frequency $\omega$ and the radius $R$ is: $\omega R=1$.

6 pp., Harvmac (l) mode