SPATIAL CORRELATION IN QUANTUM CHAOTIC SYSTEMS WITH TIME-REVERSAL SYMMETRY - THEORY AND EXPERIMENT

The correlation between the values of wave functions at two different spatial points is examined for chaotic systems with time-reversal symm etry. Employing a supermatrix method, we find that there exist long-ra nge Friedel oscillations of the wave function density for a given eige nstate, although the background wave function density fluctuates stron gly. We show that for large fluctuations, once the value of the wave f unction at one point is known, its spatial dependence becomes highly p redictable for increasingly large space around this point. These resul ts are compared with the experimental wave functions obtained from bil liard-shaped microwave cavities, and very good agreement is demonstrat ed.