TRANSITIONAL REGIONS OF FINITE FERMI SYSTEMS AND QUANTUM CHAOS

It is argued that phase transitions in finite systems are likely to exhibit level statistics ascribed to quantum chaos. Apparent counterexamples become chaotic under generic perturbation. The mathematical mechanism for this to occur lies in the abundance of exceptional points in the transitional region. Exceptional points are singularities in the complex lambda plane of the spectrum E(n)(lambda), where lambda is the parameter that effects the transition. Examples are given for illustration. It is shown that the quality of the mean field is unaffected outside the transitional region whether or not the transitional region is chaotic. Related properties of the eigenvectors are also discussed.