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

Abstract

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 ℵ N ⊥ lying on the cross-sectional planes of the cavity on the two-dimensional level number N ⊥ . We demonstrate that in the limit N ⊥ → ∞ the least squares fit of the experimental data reveals the asymptotic ratio ℵ N ⊥ / N ⊥ ≃ 0.059 ± 0.029 that is close to the theoretical prediction ℵ N ⊥ / N ⊥ ≃ 0.062 . This result is in good agreement with the predictions of percolation theory.