2-DIMENSIONAL ELECTRONS IN RANDOM MAGNETIC-FIELDS - UNIVERSALITY CLASS OF RANDOM MATRICES

An analysis is made of the statistics of energy levels for a system of an electron in a square lattice with random magnetic fields. The dens ity of states and the connected density-density correlations are calcu lated numerically for finite lattice dimension N and energy interval D elta E. Some of their characteristic features are found to agree with the predictions of an ensemble of random matrices suggested recently b y Hikami and Zee. This result might be significant because it shows th at there is a realistic physical system which is related to a non-Gaus sian matrix ensemble. Far away from the center of the spectrum. for ve ry small Delta E and very large N it is expected that the Gaussian uni tary ensemble is identical to the Hikami-Zee ensemble, so that the per tinent spectrum can be described by both of them.