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arXiv · 0903.2939

Investigation of nodal domains in a chaotic three-dimensional microwave rough billiard with the translational symmetry

Nazar Savytskyy·Oleg Tymoshchuk·Oleh Hul·Szymon Bauch·Leszek Sirko
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Abstract

We show that using the concept of the two-dimensional level number N_{|} one can experimentally study of the nodal domains in a three-dimensional (3D) microwave chaotic rough billiard with the translational symmetry. Nodal domains are regions where a wave function has a definite sign. We found the dependence of the number of nodal domains aleph_{N_{|}} lying on the cross-sectional planes of the cavity on the two-dimensional level number N_{|}. We demonstrate that in the limit N_{|} -> infinity the least squares fit of the experimental data reveals the asymptotic ratio aleph_{N_{|}}/N_{|} = 0.059 +- 0.029 that is close to the theoretical prediction aleph_{N_{|}}/N_{|} = 0.062. This result is in good agreement with the predictions of percolation theory.

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Nazar Savytskyy, Oleg Tymoshchuk, Oleh Hul, Szymon Bauch, Leszek Sirko. 2009-03-17. Investigation of nodal domains in a chaotic three-dimensional microwave rough billiard with the translational symmetry. https://doi.org/10.1016/j.physleta.2007.10.052

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