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Gaps in the spectrum of a cuboidal periodic lattice graph

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA2001YNG" target="_blank" >RIV/61988987:17310/19:A2001YNG - isvavai.cz</a>

  • Alternative codes found

    RIV/61389005:_____/19:00503691

  • Result on the web

    <a href="https://www.sciencedirect.com/science/article/pii/S0034487719300278" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0034487719300278</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/S0034-4877(19)30027-8" target="_blank" >10.1016/S0034-4877(19)30027-8</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Gaps in the spectrum of a cuboidal periodic lattice graph

  • Original language description

    We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As the main result, we find a connection between the arrangement of the gaps and the coefficients in a continued fraction associated with the ratio of edge lengths of the lattice. This knowledge enables a straightforward construction of a periodic quantum graph with any required number of spectral gaps and---to some degree---to control their positions; i.e., to partially solve the inverse spectral problem.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

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

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2019

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    REP MATH PHYS

  • ISSN

    0034-4877

  • e-ISSN

  • Volume of the periodical

    83

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    21

  • Pages from-to

    107-127

  • UT code for WoS article

    000461539000008

  • EID of the result in the Scopus database

    2-s2.0-85062272463