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

O. Hula, N. Savytskyyb, O. Tymoshchuka, S. Baucha and L. Sirkoa aInstitute of Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland bRD Vector Sp. z o.o., Krzemowa 6, 81-577 Gdynia, Poland

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Received: 19 05 2005;

We study experimentally nodal domains of wave functions (electric field 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 functionsΨN 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 domainsƝN on the level number N was found. We show that in the regimes of Breit-Wigner and Shnirelman ergodicity least squares fits of the experimental data reveal the numbers of nodal domains that in the asymptotic limit N→∞ coincide within the error limits with the theoretical predictionƝN/N≃ 0.062. Finally, we demonstrate that the signed area distributionΣA can be used as a useful criterion of quantum chaos.

DOI: 10.12693/APhysPolA.109.73 PACS numbers:05.45.Mt, 05.45.Df