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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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
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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