Scattering Phases and Density of States for Exterior Domain

1995/02/04 by J. -P. Eckmann, J.-P. Eckmann, Eckmann, J. -P. +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #chao-dyn #nlin.CD

paper · pdf · doi:10.48550/arxiv.chao-dyn/9502002

15 pages, Postscript, A4

arxiv created 1995/02/04 · openalex publication_date 1995/02/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a bounded open domain Ω∈ \real² with connected complement and piecewise smooth boundary, we consider the Dirichlet Laplacian -\DO on Ω and the S-matrix on the complement Ω^c. Using the restriction A_E of (-Δ-E)^-1 to the boundary of Ω, we establish that A_E0^-1/2A_EA_E0^-1/2-1 is trace class when E₀ is negative and give bounds on the energy dependence of this difference. This allows for precise bounds on the total scattering phase, the definition of a ζ-function, and a Krein spectral formula, which improve similar results found in the literature.

Related

• Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains
• The scattering phase: seen at last
• On the denseness of the set of scattering amplitudes
• On some bound and scattering states associated with the cosine kernel
• Determinants of Laplacians in Exterior Domains