Semiclassical density of degeneracies in a quantum regular systems

A J FENDRIK AND M J SÁNCHEZ

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL

IOP

Año: 2000 vol. 33 p. 2345 - 2350

The spectrum of eigenenergies of a quantum integrable system whose Hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings 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 calculations for two specific quantum integrable billiards.