RANDOM PERTURBATION OF SYSTEMATIC DEGENERACIES AND THEIR FOURIER-TRANSFORMS AND PERIODIC-ORBITS

The effect of random perturbation is investigated for a Hamiltonian with systematic degeneracies. It turns out that the influence of the degeneracies remains significant under perturbation. The model simulates quantized versions of classically chaotic systems in that the Fourier transform of the level density shows the characteristic lines which would be associated with the periods of periodic orbits if the system had a classical analogy. The decaying magnitude of the recurring lines is related to the spread of the probability distribution under the influence of perturbation of the degenerate levels.