Universal fluctuation of the Hall conductance in a random magnetic field

We show that the rms fluctuation of the antisymmetric part of the Hall conductance of a planar mesoscopic metal in a random magnetic field with zero average is universal; it is of the order of e²/h, independent of both the amplitude of the random magnetic field and the diffusion coefficient even in the weak-field limit. This quantity is exactly zero in the case of ordinary scalar disorder. A similar statement holds for some other systems with broken time-reversal symmetry. We propose an experiment to measure this surprising effect.