Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard
Abstract
We study experimentally nodal domains of wave functions (electric field distributions) lying in the regime of Shnirelman ergodicity in the chaotic microwave half-circular ray-splitting rough billiard. For this aim the wave functions PsiN of the billiard were measured up to the level number N=415. We show that in the regime of Shnirelman ergodicity (N>208) wave functions of the chaotic half-circular microwave ray-splitting rough billiard are extended over the whole energy surface and the amplitude distributions are Gaussian. For such ergodic wave functions the dependence of the number of nodal domains alephN on the level number N was found. We show that in the limit N->infty the least squares fit of the experimental data yields alephN/N = 0.063 +- 0.023 that is close to the theoretical prediction alephN/N = 0.062. We demonstrate that for higher level numbers N = 215-415 the variance of the mean number of nodal domains sigma2N/ N is scattered around the theoretical limit sigma2N /N = 0.05. We also found that the distribution of the areas s of nodal domains has power behavior ns ~ s-tau, where the scaling exponent is equal to tau = 2.14 +- 0.12. This result is in a good agreement with the prediction of percolation theory.