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 $U_I(q) = (ν^2/4R^2)\sin^2(q/2R)$ and the one of the particles with the pair potential $U_{II}(q) = ν^2/q^2$ and the external potential $U_{ext} = ω^2 q^2/2$. The natural relation between the frequency $ω$ and the radius $R$ is: $ωR = 1$.