On the spectrum of leaky surfaces with a potential bias

0492833 - ÚJF 2019 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Exner, Pavel
On the spectrum of leaky surfaces with a potential bias.
EMS Series of Congress Reports. The Helge Holden Anniversary Volume. Zurich: European Mathematical Society, 2018, s. 169-181. ISBN 978-3-03719-186-6.
[Conference on Non-linear PDEs, Mathematical Physics and Stochastic Analysis. Trondheim (NO), 04.07.2016-07.07.2016]
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: strong Delta-interaction * bound states * asymptotics
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

We discuss operators of the type H = -Delta + V(x) - alpha delta(x - Sigma) with an attractive interaction, alpha > 0, in L-2(R-3), where Sigma is an infinite surface, asymptotically planar and smooth outside a compact, dividing the space into two regions, of which one is supposed to be convex, and V is a potential bias being a positive constant V-0 in one of the regions and zero in the other. We find the essential spectrum and ask about the existence of the discrete one with a particular attention to the critical case, V-0 = alpha(2). We show that sigma(disc)(H) is then empty if the bias is supported in the 'exterior' region, while in the opposite case isolated eigenvalues may exist.
Trvalý link: http://hdl.handle.net/11104/0286263