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On the spectrum of leaky surfaces with a potential bias

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F18%3A00492833" target="_blank" >RIV/61389005:_____/18:00492833 - isvavai.cz</a>

  • Alternative codes found

    RIV/68407700:21340/18:00328100

  • Result on the web

    <a href="http://dx.doi.org/10.4171/186" target="_blank" >http://dx.doi.org/10.4171/186</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.4171/186" target="_blank" >10.4171/186</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On the spectrum of leaky surfaces with a potential bias

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Result continuities

  • Project

    <a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    EMS Series of Congress Reports

  • ISBN

    978-3-03719-186-6

  • ISSN

  • e-ISSN

  • Number of pages

    12

  • Pages from-to

    169-181

  • Publisher name

    European Mathematical Society

  • Place of publication

    Zurich

  • Event location

    Trondheim

  • Event date

    Jul 4, 2016

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

    000442187600009