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Wavefunction statistics in open chaotic billiards

P. W. Brouwer
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Abstract

We study the statistical properties of wavefunctions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wavefunctions cross over from real to complex. Each wavefunction is characterized by a phase rigidity, which is itself a fluctuating quantity. We calculate the probability distribution of the phase rigidity and discuss how phase rigidity fluctuations cause long-range correlations of intensity and current density. We also find that phase rigidities for wavefunctions with different incoming wave boundary conditions are statistically correlated.

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P. W. Brouwer. 2003-02-24. Wavefunction statistics in open chaotic billiards. https://doi.org/10.1103/physreve.68.046205

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