  We study the persistent current of noninteracting electrons subject to a
pointlike magnetic flux in the simply connected chaotic Robnik-Berry quantum
billiard, and also in an annular analog thereof. For the simply connected
billiard we find a large diamagnetic contribution to the persistent current at
small flux, which is independent of the flux and is proportional to the number
of electrons (or equivalently the density since we keep the area fixed). The
size of this diamagnetic contribution is much larger than mesoscopic
fluctuations in the persistent current in the simply connected billiard, and
can ultimately be traced to the response of the angular momentum $l=0$ levels
(neglected in semiclassical expansions) on the unit disk to a pointlike flux at
its center. The same behavior is observed for the annular billiard when the
inner radius is much smaller than the outer one, while the usual fluctuating
persistent current and Anderson-like localization due to boundary scattering
are seen when the annulus tends to a one-dimensional ring. We explore the
conditions for the observability of this phenomenon.
