Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation
We numerically investigate statistical properties of short-wavelength normal modes and the spectrum for the Helmholtz equation in a two-dimensional stadium-shaped region. As the geometrical optics rays within this boundary (billiards) are nonintegrable, this wave problem serves as a simple model for the study of quantum chaos. The local spatial correlation function and the probability distribution P/sub n/(psi) of wave amplitude for normal modes psi/sub n/ are computed and compared with predictions based on semiclassical arguments applied to this nonintegrable Hamiltonian. The spectrum is analyzed in terms of the probability P(..delta..E) of neighboring energy-eigenvalue separations, which is shown to be similar to a Wigner distribution for the eigenvalues of a random matrix
- Research Organization:
- Physics Department and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 5326805
- Journal Information:
- Phys. Rev. A; (United States), Vol. 37:8
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
WAVE EQUATIONS
EIGENFUNCTIONS
AMPLITUDES
ANALYTICAL SOLUTION
EIGENVALUES
PARAMETRIC ANALYSIS
PROBABILITY
TWO-DIMENSIONAL CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics