Semiclassical density of degeneracies in quantum regular systems

The spectrum of eigenenergies of a quantum integrable system whose Hamilton ian depends on a single parameter shows degeneracies (crossings) when the p arameter varies. We derive a semiclassical expression for the density of cr ossings in the plane energy-parameter, that is the number of crossings per unit of energy and unit of parameter, in terms of classical periodic orbits . We compare the results of the semiclassical formula with exact quantum ca lculations for two specific quantum integrable billiards.