Numerical experiments on the Calogero lattice

Abstract

This paper presents the results of computer experiments performed on one-dimensional, classical mechanical, N-body systems whose point particles interact pairwise via the potential V (r) =ar2+br−2, where r is interparticle distance and where a and b are positive constants. When each particle interacts with all other particles, the numerical experiments indicate that the system is mathematically integrable for either free-end or fixed-end boundary conditions. On the other hand, when each particle interacts with only its nearest neighbors, the computer detects a transition from near-integrable to stochastic behavior again for either free-end or fixed-end boundary conditions. Our results thus support the conjecture that integrability is highly sensitive to changes in the total interaction potential but insensitive to modification of boundary conditions.