Intensity statistics inside an open wave-chaotic cavity with broken time-reversal invariance.

Abstract

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density P(I) for the single-point intensity I decays as a power law for large intensities: P(I)∼I^{-(M+2)}, provided there is no internal losses. This behavior is in marked difference with the Rayleigh law P(I)∼exp(-I/I[over ¯]), which turns out to be valid only in the limit M→∞. We also find the joint probability density of intensities I_{1},...,I_{L} in L>1 observation points, and then we extract the corresponding statistics for the maximal intensity in the observation pattern. For L→∞ the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.