NU=1 2 QUANTUM HALL-EFFECT IN THE AHARONOV-CASHER GEOMETRY IN A MESOSCOPIC RING/

We study the effect of an electric charge in the middle of a ring of e lectrons in a magnetic field such as v = 1/2. In the absence of the ce ntral charge, a residual current should appear due to an Aharanov-Bohm effect. As the charge varies, periodic currents should appear in the ring. We evaluate the amplitude of these currents, as well as their pe riod as the central charge varies. The presence of these currents shou ld be a direct signature of the existence of a statistical gauge field in the v = 1/2 quantum Hall effect. Numerical diagonalizations for a small number of electrons on the sphere are also carried out. Like the mean-field results, the numerical results up to nine electrons show a nontrivial reshuffling of the ground state as the electric charge is varied.