Nodal Domains in Chaotic Microwave Rough Billiards with and without Ray-Splitting Properties

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We study experimentally nodal domains of wave functions (electric fleld distributions) lying in the regime of Breit{Wigner ergodicity in the chaotic microwave half-circular ray-splitting rough billiard. Using the rough billiard without ray-splitting properties we also study the wave functions lying in the regime of Shnirelman ergodicity. The wave functions “N of the ray-splitting billiard were measured up to the level number N = 204. In the case of the rough billiard without ray-splitting properties, the wave functions were measured up to N = 435. We show that in the regime of Breit{Wigner ergodicity most of wave functions are delocalized in the n, l basis. In the regime of Shnirelman ergodicity wave functions are homogeneously distributed over the whole energy surface. For such wave functions, lying both in the regimes of Breit{Wigner and Shnirelman ergodicity, the dependence of the number of nodal domains @N on the level number N was found. We show that in the regimes of Breit{Wigner and Shnirelman ergodicity least squares flts of the experimental data reveal the numbers of nodal domains that in the asymptotic limit N ! 1 coincide within the error limits with the theoretical prediction @N=N ’ 0:062. Finally, we demonstrate that the signed area distribution §A can be used as a useful criterion of quantum chaos.