Distribution of nearest distances between nodal points for the Berry function in two dimensions

Details Distribution of nearest distances between nodal points for the Berry function in two dimensions Distribution of nearest distances between nodal points for the Berry function in two dimensions

2000-12-10

arxiv.org/abs/nlin/0012019v1

Nonlinear Sciences

Chaotic Dynamics

11 pages, 7 figures

Scientific paper

10.1103/PhysRevE.64.036222

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 from numerical calculations for the Berry wave function.

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