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

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Hul O., Savytskyy N., Tymoshchuk O., Bauch S., Sirko L.

Acta Physica Polonica A

2006

vol. 109

issue 1

73-87

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 functionsΨ_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 domainsƝ_N 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 predictionƝ_N/N≃ 0.062. Finally, we demonstrate that the signed area distributionΣ_A can be used as a useful criterion of quantum chaos.

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1 Acta Physica Polonica A

1 2006

1 Bauch S.

1 Hul O.

1 Savytskyy N.

1 Sirko L.

1 Tymoshchuk O.

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