title: Experimental investigation of nodal domains in the chaotic microwave rough billiard.
abstract: We present the results of experimental study of nodal domains of wave functions (electric field distributions) lying in the regime of Shnirelman ergodicity in the chaotic half-circular microwave rough billiard. Nodal domains are regions where a wave function has a definite sign. The wave functions PsiN of the rough billiard were measured up to the level number N=435 . In this way the dependence of the number of nodal domains [symbol: see text]N on the level number N was found. We show that in the limit N-->infinity a least squares fit of the experimental data reveals the asymptotic number of nodal domains [symbol: see text]N/N approximately equal to 0.058+/-0.006 that is close to the theoretical prediction [symbol: see text]N/N approximately equal to 0.062 . We also found that the distributions of the areas s of nodal domains and their perimeters l have power behaviors ns is proportional to s(-tau) and nl is proportional to l(-tau'), where scaling exponents are equal to tau=1.99+/-0.14 and tau'=2.13+/-0.23 , respectively. These results are in a good agreement with the predictions of percolation theory. Finally, we demonstrate that for higher level numbers N approximately equal to 220-435 the signed area distribution oscillates around the theoretical limit SigmaA approximately 0.0386 N(-1) .
authors.affiliation: Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland.
authors.forename: Nazar
authors.initials: N
authors.lastname: Savytskyy
authors.forename: Oleh
authors.initials: O
authors.lastname: Hul
authors.forename: Leszek
authors.initials: L
authors.lastname: Sirko