WAVE-FUNCTION AND LEVEL STATISTICS OF RANDOM 2-DIMENSIONAL GAUGE-FIELDS

Level and wave-function statistics have been studied for two-dimension al clusters of the square lattice in the presence of random magnetic f luxes. Fluxes traversing lattice plaquettes are distributed uniformly between -1/2 Phi(0) and 1/2 Phi(0) with Phi(0) the flux quantum. All c onsidered statistics start close to the corresponding Wigner-Dyson dis tribution for small system sizes and monotonically move towards Poisso n statistics as the cluster size increases. Scaling is quite rapid for states close to the band edges but really difficult to observe for st ates well within the band. Localization properties are discussed consi dering two different scenarios. Experimental measurement of one of the considered statistics-wave-function statistics seems the most promisi ng one-could discern between both possibilities. A real version of the previous model, i.e., a system that is invariant under time reversal, has been studied concurrently to get coincidences and differences wit h the Hermitian model.