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The effective Hamiltonian in curved quantum waveguides under mild regularity assumptions

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F12%3A00384331" target="_blank" >RIV/61389005:_____/12:00384331 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1142/S0129055X12500183" target="_blank" >http://dx.doi.org/10.1142/S0129055X12500183</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1142/S0129055X12500183" target="_blank" >10.1142/S0129055X12500183</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    The effective Hamiltonian in curved quantum waveguides under mild regularity assumptions

  • Original language description

    The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting of the tube are considered. We show that the Laplacian converges in a norm-resolvent sense to the well-known one-dimensional Schrödinger operator whose potential is expressed in terms of the curvature of the reference curve, the twisting angle and a constant measuringthe asymmetry of the cross-section. Contrary to previous results, we allow the reference curves to have non-continuous and possibly vanishing curvature. For such curves, the distinguished Frenet frame standardly used to define the tube need not exist and, moreover, the known approaches to prove the result for unbounded tubes do not work. To establish the norm-resolvent convergence under the minimal regularity assumptions, we use an alternative frame defined by a parallel transport along

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BE - Theoretical physics

  • OECD FORD branch

Result continuities

  • Project

    Result was created during the realization of more than one project. More information in the Projects tab.

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2012

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Reviews in Mathematical Physics

  • ISSN

    0129-055X

  • e-ISSN

  • Volume of the periodical

    24

  • Issue of the periodical within the volume

    7

  • Country of publishing house

    SG - SINGAPORE

  • Number of pages

    39

  • Pages from-to

    "1250018/1"-"1250018/39"

  • UT code for WoS article

    000306590500005

  • EID of the result in the Scopus database