Scattering Phases and Density of States for Exterior Domain
Abstract
For a bounded open domain $\Omega\in \real^2$ with connected complement and piecewise smooth boundary, we consider the Dirichlet Laplacian $\DO$ on $\Omega$ and the Smatrix on the complement $\Omega^c$. Using the restriction $A_E$ of $(\DeltaE)^{1}$ to the boundary of $\Omega $, we establish that $A_{E_0}^{1/2}A_EA_{E_0}^{1/2}1$ is trace class when $E_0$ 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 $\zeta$function, and a Krein spectral formula, which improve similar results found in the literature.
 Publication:

arXiv eprints
 Pub Date:
 February 1995
 arXiv:
 arXiv:chaodyn/9502002
 Bibcode:
 1995chao.dyn..2002E
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 15 pages, Postscript, A4