Saichev A I, Berggren K F, Sadreev A F
Department of Radiophysics, Nizhny Novgorod University, Gagarin prospekt 23, 603600 Nizhny Novgorod, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036222. doi: 10.1103/PhysRevE.64.036222. Epub 2001 Aug 29.
According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that both the real and imaginary parts of the wave function are random Gaussian fields we analyze the correlation function and densities of the nodal points. Using two approaches (the Poisson and Bernoulli) we derive the distribution of nearest neighbor separations. Furthermore the distribution functions for nodal points with specific chirality are found. Comparison is made with results from numerical calculations for the Berry wave function.
根据贝里的观点，波混沌态可被视为具有随机相位和振幅的单色平面波的叠加。在此我们考虑与该状态相关的节点分布。利用波函数的实部和虚部均为随机高斯场这一性质，我们分析了节点的相关函数和密度。通过两种方法（泊松方法和伯努利方法）我们推导了最近邻间距的分布。此外，还找到了具有特定手性的节点的分布函数。并与贝里波函数的数值计算结果进行了比较。
