Abstract
We consider the Laplace-Beltrami operator in tubular neighborhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.
Originalsprache | englisch |
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Aufsatznummer | 485204 |
Fachzeitschrift | Journal of Physics A: Mathematical and Theoretical |
Jahrgang | 43 |
Ausgabenummer | 48 |
DOIs | |
Publikationsstatus | Veröffentlicht - 3 Dez. 2010 |
Extern publiziert | Ja |
ASJC Scopus subject areas
- Statistische und nichtlineare Physik
- Statistik und Wahrscheinlichkeit
- Modellierung und Simulation
- Mathematische Physik
- Allgemeine Physik und Astronomie