Influence of intermittency on quantum spectra

Abstract

Bound chaotic systems typically exhibit intermittency. Some semiclassical properties of intermittency are studied. The hyperbola billiard and the x2y2 model are used as strongly intermittent model systems. The almost integrable motion in the arms of the potential may be treated in the adiabatic approximation. The corresponding adiabatic Hamiltonian may be semiclassically quantized, yielding surprisingly good agreement for the hyperbola billiard. It is then demonstrated, by means of the semiclassical trace formula, how this result may be related to families of periodic orbit exclusively exploring the potential arms. It is discussed how this result implies an integrable component in the spectrum. Possible implications for the resummation problem of the trace formula, as well as for the statistical properties of energy levels, are discussed.