期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 43, 期 48, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/43/48/485204
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资金
- Czech Ministry of Education, Youth and Sports [LC06002]
- CTU [CTU0910114]
- Grant Agency of the Czech Republic [202/08/H072]
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-Hermitianm-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.
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