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PT-symmetric models in curved manifolds
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SYSNO ASEP 0351846 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název PT-symmetric models in curved manifolds Tvůrce(i) Krejčiřík, David (UJF-V) RID
Siegl, Petr (UJF-V) RIDZdroj.dok. Journal of Physics A-Mathematical and Theoretical. - : Institute of Physics Publishing - ISSN 1751-8113
Roč. 43, č. 48 (2010), 485204/1-485204/30Poč.str. 30 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova NON-HERMITIAN HAMILTONIANS ; SCHRODINGER-TYPE OPERATORS ; PSEUDO-HERMITICITY Vědní obor RIV BA - Obecná matematika CEP LC06002 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000284263800013 DOI 10.1088/1751-8113/43/48/485204 Anotace 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. Pracoviště Ústav jaderné fyziky Kontakt Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Rok sběru 2011
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