Monday, March 12, 2012

1203.2098 (Pavel Exner et al.)

Spectral estimates for Dirichlet Laplacians and Schroedinger operators
on geometrically nontrivial cusps
   [PDF]

Pavel Exner, Diana Barseghyan
The goal of this paper is to derive estimates of eigenvalue moments for Dirichlet Laplacians and Schr\"odinger operators in regions having infinite cusps which are geometrically nontrivial being either curved or twisted; we are going to show how those geometric properties enter the eigenvalue bounds. The obtained inequalities reflect the essentially one-dimensional character of the cusps and we give an example showing that in an intermediate energy region they can be much stronger than the usual semiclassical bounds.
View original: http://arxiv.org/abs/1203.2098

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