turn to semiclassical correspondences, where we use a phase-space approach to the quantum eigenfunctions, and make direct connections with various types of classical phase space periodic orbits. In section V we discuss possible experimental scenarios where the predicted effects may be observable. Finally, in section VI we summarize our results and present our conclusions.

The Model {#sec:model}
=========

The model of a quantum dot we consider here is that of an electron confined to a disk of radius $R_0$ subject to steady ([*d.c.*]{}) and time-periodic ([*a.c.*]{}) magnetic fields. Choosing the cylindrical gauge, where the vector potential ${\bf A}(\vec \rho,t) 
= {1\over 2}B(t)\, \rho\, \hat e_\phi$, $B(t)$ being the time-dependent magnetic field, the quantum mechanical single-particle Hamiltonian in the coordinate representation is given by $$\label{eq:a}
H = -\frac{{\hbar^2}}{2m^*}\left( \frac{d^2}{d\rho^2} + 
\frac{1}{\rho}\frac{d}{d\rho} + 
\frac{1}{\rho^2}\frac{d^2}{d\phi^2} \right) + \frac{1}{8} m^* 
\Omega^2(t) \rho^2 + \frac{1}{2} \Omega(t) L_z, \quad 0 \leq 
\rho \leq R_0,$$ where $m^*$ is the effective mass of the electron (roughly 0.067$m_e$ in GaAs-AlGaAs semiconductor quantum dots) [@beenakker], $L_z$ is the operator of the conserved angular momentum, and $\Omega(t) = e^{*}B(t)/m^*c$, $e^{*}$ and $c$ being the effective electronic charge ($e^{*}\sim 0.3e$) and the speed of light, respectively. Let the magnetic field be of 