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

• Authors: O. Hul , N. Savytskyy , O. Tymoshchuk , S. Bauch , L. Sirko
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

05.45.Mt; 05.45.Df

Discipline

• 05.45.Df: Fractals(see also 47.53.+n Fractals in fluid dynamics; 61.43.Hv Fractals; macroscopic aggregates in structure of solids)
• 05.45.Mt: Quantum chaos; semiclassical methods

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2006
• Volume: 109
• Issue: 1
• Pages: 73-87

Dates

published

2006-01

received

2005-05-19

Contributors

author

O. Hul

• Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland

author

N. Savytskyy

• RD Vector Sp. z o.o., Krzemowa 6, 81-577 Gdynia, Poland

author

O. Tymoshchuk

• Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland

author

S. Bauch

• Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland

author

L. Sirko

• Institute of Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland

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Identifiers

DOI

10.12693/APhysPolA.109.73