Quantum eigenstates of a strongly chaotic system and the scar phenomenon

The quantum eigenstates of the Hadamard-Gutzwiller model, a strongly chaotic system, are studied with special emphasis on the scar phenomenon. The dynamics of a localized wavepacket is discussed which travels along a short periodic orbit yielding a test for the scar model developed by Heller. The autocorrelation function C(t) and the smeared weighted spectral density Sg (E) are in accordance with this model, but the conclusion that this implies the existence of scarred eigenstates is not confirmed. A random wavefunction model generates with the same probability intensity structures being localized near short periodic orbits as the wavefunctions obeying the Schrödinger equation. Although there are some eigenstates which are localized near a periodic orbit, the conclusion that their intensities differ significantly from the statistically expected ones cannot be drawn. Thus the scar phenomenon seems to be absent in the Hadamard-Gutzwiller model.