Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation

Journal Article · Fri Apr 15 04:00:00 EDT 1988 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.37.3067· OSTI ID:5326805

McDonald, S W; Kaufman, A N

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), Journal Name: Phys. Rev. A; (United States) Vol. 37:8; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
EIGENVALUES
EQUATIONS
FUNCTIONS
PARAMETRIC ANALYSIS
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
TWO-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS