  We study the classical and quantum mechanics of a free particle that collides
elastically with the walls of a circular disk with the radius varying
periodically in time. The quasi-energy spectral properties of the model are
obtained from evaluation of finite-dimensional approximations to the time
evolution operator. As the scaled hbar is changed from large to small, the
statistics of the Quasienergy Eigenvalues (QEE) change from Poisson to circular
orthogonal ensemble (COE). Different statistical tests are used to characterize
this transition. The transition of the Quasienergy Eigenfunctions (QEF) is also
studied using the chi-squared test with nu degrees of freedom, which goes over
to the Porter-Thomas distribution for nu=1. We find that the integrable regime
is associated with exponentially localized QEF whereas the eigenfunctions are
extended in the chaotic, COE regime. We change the representation of the model
to one in which the boundary is fixed and the Hamiltonian acquires a quadratic
forcing term. We then carry out a successful comparison between specific
classical phase space solutions and their corresponding QEFs in the Husimi
representation.
