INTERIOR DIRICHLET EIGENVALUE PROBLEM, EXTERIOR NEUMANN SCATTERING PROBLEM, AND BOUNDARY-ELEMENT METHOD FOR QUANTUM BILLIARDS

Authors
TASAKI S HARAYAMA T SHUDO A
Citation
S. Tasaki et al., INTERIOR DIRICHLET EIGENVALUE PROBLEM, EXTERIOR NEUMANN SCATTERING PROBLEM, AND BOUNDARY-ELEMENT METHOD FOR QUANTUM BILLIARDS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(1), 1997, pp. 13-16
Citations number
23
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
Journal title
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics → ACNP
ISSN journal
1063651X
Volume
56
Issue
1
Year of publication
1997
Part
A
Pages
13 - 16
Database
ISI
SICI code
1063-651X(1997)56:1<13:IDEPEN>2.0.ZU;2-I
Abstract
An explicit expression for the Fredholm determinant D(E) appearing in the boundary element method for two-dimensional quantum billiards is d erived in terms of the interior Dirichlet eigenenergies and exterior N eumann scattering phase shifts. Not only in the semiclassical regime b ut also in ail order of (h) over bar, D(E) admits the factorization in to the interior and exterior contributions, where the former has zeros at interior Dirichlet eigenenergies and the latter at resonances of t he Neumann scattering. A new aspect of the Kac's inverse problem is al so discussed.