Near-integrable systems: Resonances and semiclassical trace formulas

Trace formulas relate the quantum density of states to the properties of the periodic orbits of the underlying classical system. The resulting expressions depend critically on the nature of the dynamics and whether the orbits are stable or unstable. Several open questions exist for the class of classical systems that are near integrability. The most important consequence of a generic perturbation to an integrable system is the creation of resonances. We derive generalized expressions appropriate for resonances and apply them to a system that can be taken as a paradigm for the transition from regular to chaotic dynamics. © 1996 The American Physical Society.