Some examples in one-dimensional ''geometric'' scattering on manifolds

[摘要] 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. (C) 1997 Academic Press.

[发布日期] 1997-08-01