Statistical wave field theory: Anisotropic wave fields under Neumann's boundary condition

Area of Science:

• Mathematical Physics
• Acoustics
• Wave Phenomena

Background:

• The statistical wave field theory describes wave behavior in bounded domains.
• Previous work focused on diffuse fields (mixing rooms) and anisotropic fields (special polyhedra).
• Existing theories rely on dynamical billiards, Weyl-like laws, or crystallographic approaches.

Purpose of the Study:

• To introduce a unified statistical wave field theory for semi-mixing billiards.
• To analyze the wave field's statistical properties under Neumann boundary conditions.
• To investigate the anisotropy and spatial correlations of the wave field.

Main Methods:

• Development of a unified theoretical framework for semi-mixing billiards.
• Application of mathematical crystallography and geometric approaches.
• Analysis of wave field stationarity and anisotropy.

Main Results:

• The unified theory provides closed-form expressions for power distribution and correlations.
• Wave fields in semi-mixing billiards with Neumann conditions are stationary but generally anisotropic.
• Spatial correlations deviate from the cardinal sine formula characteristic of diffuse fields.

Conclusions:

• The unified theory offers a more general approach to wave field analysis in bounded domains.
• The findings highlight the anisotropic nature of wave fields in semi-mixing billiards.
• This work extends the applicability of statistical wave field theory to a broader class of geometries.