Wave function statistics in open chaotic billiards

2003/02/24 by Piet W. Brouwer, P. W. Brouwer
Physics and Astronomy · #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Theoretical and Computational Physics #cond-mat.mes-hall #nlin.CD

paper · pdf · doi:10.1103/physreve.68.046205

published as Phys. Rev. E 68, 046205 (2003) · 4 pages, RevTeX; 1 figure

arxiv created 2003/02/24 · openalex publication_date 2003/10/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the statistical properties of wave functions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wave functions cross over from real to complex. Each wave function 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 wave functions with different incoming wave boundary conditions are statistically correlated.

Citations

• Distribution of the quantum mechanical time-delay matrix for a chaotic cavity
• Statistical properties of many-particle spectra V. Fluctuations and symmetries

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