Some Examples in One-Dimensional “Geometric” Scattering on Manifolds

✍ Scribed by Alexander Kiselev

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 246 KB
• Volume: 212
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5497

✦ Synopsis

We consider ''geometric'' scattering for a Laplace᎐Beltrami operator on a compact Riemannian manifold inserted between ''wires,'' that is, two half-lines. We discuss applicability and correctness of this model. With an example, we show that such a scattering problem may exhibit unusual properties: the transition coefficient has a sequence of sharp peaks which become more and more distant at high energy and otherwise turns to zero.