A lower bound to the spectral threshold in curved tubes
Mathematical Physics
2009-11-10 v1 Mesoscale and Nanoscale Physics
math.MP
Spectral Theory
Quantum Physics
Abstract
We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.
Cite
@article{arxiv.math-ph/0405039,
title = {A lower bound to the spectral threshold in curved tubes},
author = {P. Exner and P. Freitas and D. Krejcirik},
journal= {arXiv preprint arXiv:math-ph/0405039},
year = {2009}
}
Comments
LaTeX, 13 pages; to appear in R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci