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Bound states in point-interaction star graphs

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F01%3A00000744" target="_blank" >RIV/61389005:_____/01:00000744 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Bound states in point-interaction star graphs

  • Original language description

    We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a fixed spacingbetween the interaction sites. We prove that the essential spectrum of this system is the same as that of the infinite straight 'polymer', but in addition there are isolated eigenvalues unless N = 2 and the graph is a straight line. We also show that thesystem has many strongly bound states if at least one of the angles between the star arms is small enough. Examples of eigenfunctions and eigenvalues are computed numerically.

  • Czech name

    Vázané stavy v hvězdicovitých grafech bodových interakcí

  • Czech description

    Diskutujeme diskrétní spektrum Hamiltoniánu popisujícího dvourozměrnou kvantovou částici interagující s nekonečnou množinou bodových interakcí. Předpokládáme, že tato je umístěna do hvězdicového grafu.

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

    <a href="/en/project/IAA1048801" target="_blank" >IAA1048801: Constraint quantum systems</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2001

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Journal of Physics. A - Mathematical and General Physics

  • ISSN

    0305-4470

  • e-ISSN

  • Volume of the periodical

    34

  • Issue of the periodical within the volume

    38

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    11

  • Pages from-to

    7783-7794

  • UT code for WoS article

  • EID of the result in the Scopus database