Elizaveta Safonova: Intensity statistics inside an open wave-chaotic cavity with broken time-reversal invariance

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 powerlaw for large intensities: P(I) ∼ I −(M+2), provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law P(I) ∼ exp(−I/I) which turns out to be valid only in the limit M → ∞. We also find the joint probability density of intensities I1, . . . , IL in L > 1 observation points, and then 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.