Quantum graphs with the Bethe-Sommerfeld property

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00480621" target="_blank" >RIV/61389005:_____/17:00480621 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21340/17:00319051

Result on the web

<a href="http://dx.doi.org/10.17586/2220-8054-2017-8-3-305-309" target="_blank" >http://dx.doi.org/10.17586/2220-8054-2017-8-3-305-309</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.17586/2220-8054-2017-8-3-305-309" target="_blank" >10.17586/2220-8054-2017-8-3-305-309</a>

Result language

angličtina

Original language name

Quantum graphs with the Bethe-Sommerfeld property

Original language description

In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of graph Hamiltonians, being generic in a sense, inspires the question about the existence of graphs with a finite and nonzero number of spectral gaps. We show that the answer depends on the vertex couplings together with commensurability of the graph edges. A finite and nonzero number of gaps is excluded for graphs with scale invariant couplings. On the other hand, we demonstrate that graphs featuring a finite nonzero number of gaps do exist, illustrating the claim on the example of a rectangular lattice with a suitably tuned delta-coupling at the vertices.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

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

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)

Publication year

2017

Confidentiality

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

Name of the periodical

Nanosystems: Physics, Chemistry, Mathematics

ISSN

2220-8054

e-ISSN

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Volume of the periodical

8

Issue of the periodical within the volume

3

Country of publishing house

RU - RUSSIAN FEDERATION

Number of pages

5

Pages from-to

305-309

UT code for WoS article

000412772400001

EID of the result in the Scopus database

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