Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard

Details Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard

2009-03-12

arxiv.org/abs/0903.2129v1

Phys. Rev. E 72, 066212 (2005)

Nonlinear Sciences

Chaotic Dynamics

16 pages, 8 figures

Scientific paper

10.1103/PhysRevE.72.066212

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 Psi_N 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 aleph_N on the level number N was found. We show that in the limit N->infty the least squares fit of the experimental data yields aleph_N/N = 0.063 +- 0.023 that is close to the theoretical prediction aleph_N/N = 0.062. We demonstrate that for higher level numbers N = 215-415 the variance of the mean number of nodal domains 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 has power 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 of percolation theory.

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