  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, which
gives rise to non-commuting kinetic momenta. The two-dimensional electron gas
is described as a 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 coordinates do not commute. The non-commutativity of coordinates
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. The proposed
theory may explain the experimental results recently reported by J. Zhang et
al.
