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PT-symmetric models in curved manifolds
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SYSNO ASEP 0351846 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title PT-symmetric models in curved manifolds Author(s) Krejčiřík, David (UJF-V) RID
Siegl, Petr (UJF-V) RIDSource Title Journal of Physics A-Mathematical and Theoretical. - : Institute of Physics Publishing - ISSN 1751-8113
Roč. 43, č. 48 (2010), 485204/1-485204/30Number of pages 30 s. Language eng - English Country GB - United Kingdom Keywords NON-HERMITIAN HAMILTONIANS ; SCHRODINGER-TYPE OPERATORS ; PSEUDO-HERMITICITY Subject RIV BA - General Mathematics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000284263800013 DOI 10.1088/1751-8113/43/48/485204 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2011
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