QUANTUM MANIFESTATIONS OF CLASSICAL CHAOS IN A FERMI ACCELERATING DISK

We study the classical and quantum mechanics of a two-dimensional vers ion of a Fermi accelerator. The model consists of a free particle that collides elastically with the walls of a circular disk with the radiu s varying periodically in time. A complete quantum mechanical solution of the problem is possible for a specific choice of the time-periodic oscillating radius. The quasi-energy spectral properties of the model are obtained from direct evaluation of finite-dimensional approximati ons to the time evolution operator. As the scaled h is changed from la rge to small the statistics of the Quasienergy Eigenvalues (QEE) chang e from Poisson to circular orthogonal ensemble (COE). Different statis tical tests are used to characterize this transition. The transition o f the Quasienergy Eigenfunctions (QEF) is also studied using the chi(2 ) test with v degrees of freedom. The Porter-Thomas distribution is sh own to apply in the COE regime, while the Poisson regime does not fit the chi(2) test with v = 0. We find that the Poisson regime is associa ted with exponentially localized QEF whereas the eigenfunctions are ex tended in the COE regime. To make a direct comparison between the clas sical and quantum solutions we change the representation of the model to one in which the boundary is fixed and the Hamiltonian acquires a q uadratic term with a time-periodic frequency. We then carry out a succ essful comparison between specific classical phase space surface-of-se ction solutions and their corresponding quasi-energy eigenfunctions in the Husimi representation.