Probability Amplitude Fluctuations in Experimental Wave Chaotic Eigenmodes with and Without Time-Reversal Symmetry

Abstract

We have measured the probability density $|\ensuremath{\psi}(r){|}^{2}$ in the semiclassical limit of a classically chaotic square well potential with and without time reversal symmetry, and compared our findings with theoretical predictions. We find that wave functions with time-reversal symmetry have larger fluctuations than those without time-reversal symmetry. To quantify the degree of these fluctuations, eigenmodes both with and without time-reversal symmetry are statistically analyzed and the two-point spatial correlation function and the probability density distribution function of the eigenmodes are found to agree with theoretical predictions.