Bound states in a locally deformed waveguide: the critical case
| dc.creator | Exner, P. | |
| dc.creator | Vugalter, S. A. | |
| dc.date | 1996-01-23 | |
| dc.date.accessioned | 2026-07-07T09:13:35Z | |
| dc.date.available | 2026-07-07T09:13:35Z | |
| dc.description | We consider the Dirichlet Laplacian for a strip in $\,\R^2$ with one straight boundary and a width $\,a(1+λf(x))\,$, where $\,f\,$ is a smooth function of a compact support with a length $\,2b\,$. We show that in the critical case, $\,\int_{-b}^b f(x)\, dx=0\,$, the operator has no bound states for small $\,|λ|\,$ if $\,b<(\sqrt{3}/4)a\,$. On the other hand, a weakly bound state exists provided $\,\|f'\|< 1.56 a^{-1}\|f\|\,$; in that case there are positive $\,c_1, c_2\,$ such that the corresponding eigenvalue satisfies $\,-c_1λ^4\le ε(λ)- (π/a)^2 \le -c_2λ^4\,$ for all $\,|λ|\,$ sufficiently small. | |
| dc.description | LaTeX file, 9 pages, to appear in Lett. Math. Phys | |
| dc.identifier | https://arxiv.org/abs/funct-an/9601002 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9601002 | |
| dc.identifier | Lett. Math. Phys. 39 (1997), 59-68 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152376 | |
| dc.subject | Functional Analysis | |
| dc.subject | Condensed Matter | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Physics | |
| dc.title | Bound states in a locally deformed waveguide: the critical case | |
| dc.type | text |