Maksimov Dmitrii N, Sadreev Almas F
Institute of Physics, Academy of Sciences, 660036 Krasnoyarsk, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):056204. doi: 10.1103/PhysRevE.77.056204. Epub 2008 May 8.
We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.
我们考虑平面内矢量位移(u = (u, v))的节点（NPs）(u = 0)和(v = 0)，该矢量位移服从纳维 - 柯西方程。类似于量子混沌的贝里猜想，我们将混沌台球的平面内本征态表示为具有随机相位的纵向和横向平面波叠加的实部。通过对随机相位求平均，我们推导出了节点的平均密度和关联函数。因此，我们考虑节点之间最近距离的分布。
