# Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard - Nonlinear Sciences > Chaotic Dynamics

Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard - Nonlinear Sciences > Chaotic Dynamics - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study experimentally nodal domains of wave functions electric fielddistributions lying in the regime of Shnirelman ergodicity in the chaoticmicrowave half-circular ray-splitting rough billiard. For this aim the wavefunctions Psi N of the billiard were measured up to the level number N=415. Weshow that in the regime of Shnirelman ergodicity N>208 wave functions of thechaotic half-circular microwave ray-splitting rough billiard are extended overthe whole energy surface and the amplitude distributions are Gaussian. For suchergodic wave functions the dependence of the number of nodal domains aleph N onthe level number N was found. We show that in the limit N->infty the leastsquares fit of the experimental data yields aleph N-N = 0.063 +- 0.023 that isclose to the theoretical prediction aleph N-N = 0.062. We demonstrate that forhigher level numbers N = 215-415 the variance of the mean number of nodaldomains sigma^2 N- N is scattered around the theoretical limit sigma^2 N -N =0.05. We also found that the distribution of the areas s of nodal domains haspower behavior n s ~ s^{-tau}, where the scaling exponent is equal to tau =2.14 +- 0.12. This result is in a good agreement with the prediction ofpercolation theory.

Author: ** Oleh Hul, Nazar Savytskyy, Oleg Tymoshchuk, Szymon Bauch, Leszek Sirko**

Source: https://arxiv.org/