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

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 ℵN⊥ 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 ℵN⊥/N⊥≃0.059±0.029 that is close to the theoretical prediction ℵN⊥/N⊥≃0.062. This result is in good agreement with the predictions of percolation theory.