Semiclassical Trace Formulas of Near-Integrable Systems: Resonances

Abstract

Trace formulas relate the quantum density of states to the properties of the periodic orbits of the underlying classical system. The expressions depend critically on the nature of the classical dynamics. The near-integrable regime is most importantly characterized by the destruction of rational invariant tori being replaced by chains of resonances, yet without globalized chaos being introduced. We give new, generalized expressions appropriate for resonances and apply them to a system that has served as a paradigm for the transition from regular to chaotic dynamics.