标题： 混沌微波射线分裂粗糙台球中的节点域研究 显示英文标题

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

摘要： 我们实验研究了处于Shnirelman遍历性区域内的波函数（电场分布）的节点域，在混沌微波半圆形射线分裂粗糙板中。 为此，测量了该板的波函数Psi_N，直到能级数N=415。 我们表明，在Shnirelman遍历性区域（N>208）内，混沌半圆形微波射线分裂粗糙板的波函数扩展在整个能量表面上，振幅分布是高斯分布的。 对于这种遍历性波函数，发现了节点域数量aleph_N与能级数N之间的依赖关系。 我们表明，在N->infty极限下，实验数据的最小二乘拟合得到aleph_N/N = 0.063 +- 0.023，这接近理论预测aleph_N/N = 0.062。 我们证明，对于更高的能级数N = 215-415，平均节点域数的方差sigma^2_N/ N围绕理论极限sigma^2_N /N = 0.05波动。 我们还发现，节点域面积s的分布具有幂律行为n_s ~ s^{-tau}，其中标度指数等于tau = 2.14 +- 0.12。 这一结果与渗透理论的预测有很好的一致性。 显示英文摘要

摘要： 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.