Quantum graphs with the Bethe-Sommerfeld property

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/17:00319051

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum graphs with the Bethe-Sommerfeld property

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Quantum graphs with the Bethe-Sommerfeld property

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GA17-01706S" target="_blank" >GA17-01706S: Matematicko-fyzikální modely nových materiálů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Nanosystems: Physics, Chemistry, Mathematics

ISSN

2220-8054

e-ISSN

—

Svazek periodika

8

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

RU - Ruská federace

Počet stran výsledku

5

Strana od-do

305-309

Kód UT WoS článku

000412772400001

EID výsledku v databázi Scopus

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