CLASSICAL AND QUANTUM CHAOS IN A QUANTUM-DOT IN TIME-PERIODIC MAGNETIC-FIELDS

We investigate the classical and quantum dynamics of an electron confi ned to a circular quantum dot in the presence of homogeneous B-dc+B-ac magnetic fields. The classical motion shows a transition to chaotic b ehavior depending on the ratio epsilon=B-ac/B-dc of field magnitudes a nd the cyclotron frequency <(omega)over tilde (c)> in units of the dri ve frequency. We determine a phase boundary between regular and chaoti c classical behavior in the epsilon vs <(omega)over tilde (c)> plane. In the quantum regime we evaluate the quasienergy spectrum of the time -evolution operator. We show that the nearest-neighbor quasienergy eig envalues show a transition from level clustering to level repulsion as one moves from the regular to chaotic regime in the (epsilon, <(omega )over tilde (c)>) plane. The Delta(3) statistic confirms this transiti on. In the chaotic regime, the eigenfunction statistics coincides with the Porter-Thomas prediction. Finally, we explicitly establish the ph ase-space correspondence between the classical and quantum solutions v ia the Husimi phase-space distributions of the model. Possible experim entally feasible conditions to see these effects are discussed.