On the equilibrium properties of confined one-dimensional systems

In this work Ne consider a purely classical one-dimensional system of N ide ntical point particles, repelling each other through a convex potential ene rgy, and confined to a segment by a strictly convex external potential. We prove that such a system admits one and only one stable equilibrium configu ration. This result is an example of dimension-dependent property. In fact, as is well known, confined systems in two and three dimensions exhibit, in general, under the same assumptions, a variety of stable states.