  We present results of a detailed quantum mechanical study of a gas of $N$
noninteracting electrons confined to a circular boundary and subject to
homogeneous dc plus ac magnetic fields $(B=B_{dc}+B_{ac}f(t)$, with
$f(t+2\pi/\omega_0)=f(t)$). We earlier found a one-particle {\it classical}
phase diagram of the (scaled) Larmor frequency
$\tilde\omega_c=omega_c/\omega_0$ {\rm vs} $\epsilon=B_{ac}/B_{dc}$ that
separates regular from chaotic regimes. We also showed that the quantum
spectrum statistics changed from Poisson to Gaussian orthogonal ensembles in
the transition from classically integrable to chaotic dynamics. Here we find
that, as a function of $N$ and $(\epsilon,\tilde\omega_c)$, there are clear
quantum signatures in the magnetic response, when going from the
single-particle classically regular to chaotic regimes. In the quasi-integrable
regime the magnetization non-monotonically oscillates between diamagnetic and
paramagnetic as a function of $N$. We quantitatively understand this behavior
from a perturbation theory analysis. In the chaotic regime, however, we find
that the magnetization oscillates as a function of $N$ but it is {\it always}
diamagnetic. Equivalent results are also presented for the orbital currents. We
also find that the time-averaged energy grows like $N^2$ in the
quasi-integrable regime but changes to a linear $N$ dependence in the chaotic
regime. In contrast, the results with Bose statistics are akin to the
single-particle case and thus different from the fermionic case. We also give
an estimate of possible experimental parameters were our results may be seen in
semiconductor quantum dot billiards.
