  We investigate the effect of a microwave field on a confined two dimensional
electron gas which contains an insulating region comparable to the Fermi
wavelength. The insulating region causes the electron wave function to vanish
in that region. We describe the insulating region as a static vortex. The
vortex carries a flux which is determined by vanishing of the charge density of
the electronic fluid due to the insulating region. The sign of the vorticity
for a hole is opposite to the vorticity for adding additional electrons. The
vorticity gives rise to non-commuting kinetic momenta. The two dimensional
electron gas is described as fluid with a density which obeys the Fermi-Dirac
statistics. The presence of the confinement potential gives rise to vanishing
kinetic momenta in the vicinity of the classical turning points. As a result,
the Cartesian coordinate do not commute and gives rise to a Hall current which
in the presence of a modified Fermi-Surface caused by the microwave field
results in a rectified voltage. Using a Bosonized formulation of the two
dimensional gas in the presence of insulating regions allows us to compute the
rectified current. The proposed theory may explain the experimental results
recently reported by J. Zhang et al.
