QUANTUM SIGNATURE OF A PERIOD-DOUBLING BIFURCATION AND SCARS OF PERIODIC-ORBITS

The density of states is numerically calculated for a nonintegrable Hamiltonian whose shortest-periodic-orbit family undergoes a period-doubling bifurcation in the energy interval considered. Smoothing the density using a suitable width deltaE, oscillations are observed due to only the family of shortest periods or also its period doubling. The period-doubling resonance results in a higher average amplitude of the corresponding spectral oscillations than for the primitive orbit. The main periodic families produce strong scars in the wave intensities. Projections of the Husimi distributions also exhibit scars that are, however, not so clear.