Classical and quantum chaos in a quantum dot in time-periodic magnetic fields

We investigate the classical and quantum dynamics of an electron confined to a circular quantum dot in the presence of homogeneous ${\mathit{B}}_{\mathrm{dc}}$+${\mathit{B}}_{\mathrm{ac}}$ magnetic fields. The classical motion shows a transition to chaotic behavior depending on the ratio ε=${\mathit{B}}_{\mathrm{ac}}$/${\mathit{B}}_{\mathrm{dc}}$ of field magnitudes and the cyclotron frequency ω${\mathrm{̃}}_{\mathit{c}}$ in units of the drive frequency. We determine a phase boundary between regular and chaotic classical behavior in the ε vs ω${\mathrm{̃}}_{\mathit{c}}$ plane. In the quantum regime we evaluate the quasienergy spectrum of the time-evolution operator. We show that the nearest-neighbor quasienergy eigenvalues show a transition from level clustering to level repulsion as one moves from the regular to chaotic regime in the (ε,ω${\mathrm{̃}}_{\mathit{c}}$) plane. The ${\mathrm{\Delta }}_3$ statistic confirms this transition. In the chaotic regime, the eigenfunction statistics coincides with the Porter-Thomas prediction. Finally, we explicitly establish the phase-space correspondence between the classical and quantum solutions via the Husimi phase-space distributions of the model. Possible experimentally feasible conditions to see these effects are discussed. © 1996 The American Physical Society.