QUANTUM EIGENSTATES OF A STRONGLY CHAOTIC SYSTEM AND THE SCAR PHENOMENON

The quantum eigenstates of the Hadamard-Gutzwiller model, a strongly c haotic system, are studied with special emphasis on the scar phenomeno n. The dynamics of a localized wavepacket is discussed which travels a long a short periodic orbit yielding a test for the scar model develop ed by Heller. The autocorrelation function C(t) and the smeared weight ed spectral density S-g(E) are in accordance with this model, but the conclusion that this implies the existence of scarred eigenstates is n ot confirmed. A random wavefunction model generates with the same prob ability intensity structures being localized near short periodic orbit s as the wavefunctions obeying the Schrodinger equation. Although ther e are some eigenstates which are localized near a periodic orbit, the conclusion that their intensities differ significantly from the statis tically expected ones cannot be drawn. Thus the scar phenomenon seems to be absent in the Hadamard-Gutzwiller model.