# Experimental investigation of nodal domains in the chaotic microwave rough billiard

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- Published Article
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- DOI: 10.1103/PhysRevE.70.056209
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- arXiv
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## 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 Psi_N of the rough billiard were measured up to the level number N=435. In this way the dependence of the number of nodal domains \aleph_N on the level number $N$ was found. We show that in the limit N->infty a least squares fit of the experimental data reveals the asymptotic number of nodal domains aleph_N/N = 0.058 +- 0.006 that is close to the theoretical prediction aleph_N/N +- 0.062. We also found that the distributions of the areas s of nodal domains and their perimeters l have power behaviors n_s ~ s^{-tau} and n_l ~ 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 = 220-435 the signed area distribution oscillates around the theoretical limit Sigma_{A} = 0.0386 N^{-1}.