Chaos in a quantum dot\
    in time-periodic magnetic fields
---

Introduction {#sec:intro}
============

In this paper, we present results of a study of the behavior of an electron confined to a disk of finite radius, subjected to spatially uniform, constant ($B_{dc}$) plus time-varying ($B_{ac}$) perpendicular magnetic fields. This allows us to analyze an old problem which exhibits some very novel behavior because of the time-dependent field. Without this time varying component of the field, the electronic states form the oscillator-like Landau levels[@fock]. With the addition of confinement, this constant field problem was studied in great detail by Dingle[@dingle]. He obtained perturbative solutions and subsequently others obtained numerical and exact[@robnik] solutions. The solutions depend on the ratio of the cyclotron radius $\rho_c$ to the confinement radius $R_0$. One of the most important consequences of confinement is the presence of ‘skipping orbits’, which play an important role, for example, in the Quantum Hall Effect[@prange].

This problem is of significant interest as a consequence of two independent developments over the past few years. One, the important advances in our knowledge of classical chaos[@ll], and to a lesser extent, it’s quantum and semiclassical counterparts[@casati1]; and two, the spectacular advances in the fabrication of very 