Počet záznamů: 1
PT-symmetric models in curved manifolds
0351846 - UJF-V 2011 RIV GB eng J - Článek v odborném periodiku
Krejčiřík, David - Siegl, Petr
PT-symmetric models in curved manifolds.
Journal of Physics A-Mathematical and Theoretical. Roč. 43, č. 48 (2010), 485204/1-485204/30 ISSN 1751-8113
Grant CEP: GA MŠk LC06002
Výzkumný záměr: CEZ:AV0Z10480505
Klíčová slova: NON-HERMITIAN HAMILTONIANS * SCHRODINGER-TYPE OPERATORS * PSEUDO-HERMITICITY
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.641, rok: 2010
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.
Trvalý link: http://hdl.handle.net/11104/0191502