Asymptotics of Resonances Induced by Point Interactions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00484314" target="_blank" >RIV/61389005:_____/17:00484314 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.12693/APhysPolA.132.1677" target="_blank" >http://dx.doi.org/10.12693/APhysPolA.132.1677</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.12693/APhysPolA.132.1677" target="_blank" >10.12693/APhysPolA.132.1677</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotics of Resonances Induced by Point Interactions

Popis výsledku v původním jazyce

We consider the resonances of the self-adjoint three-dimensional Schrodinger operator with point interactions of constant strength supported on the set X = {x(n)}(n-1)(N). The size of X is defined by V-X = max pi is an element of Pi(N) Sigma(N)(n = 1) vertical bar x(n) - x(pi(n))vertical bar, where Pi(N) is the family of all the permutations of the set {1, 2, ... N}. We prove that the number of resonances counted with multiplicities and lying inside the disc of radius R behaves asymptotically linear W-X is an element of R + O(1) as R -> infinity, where the constant W-X is an element of[0, V-X] can be seen as the effective size of X. Moreover, we show that there exist a configuration of any number of points such that W-X = V-X. Finally, we construct an example for N = 4 with W-X < V-X, which can be viewed as an analogue of a quantum graph with non-Weyl asymptotics of resonances.

Název v anglickém jazyce

Asymptotics of Resonances Induced by Point Interactions

Popis výsledku anglicky

We consider the resonances of the self-adjoint three-dimensional Schrodinger operator with point interactions of constant strength supported on the set X = {x(n)}(n-1)(N). The size of X is defined by V-X = max pi is an element of Pi(N) Sigma(N)(n = 1) vertical bar x(n) - x(pi(n))vertical bar, where Pi(N) is the family of all the permutations of the set {1, 2, ... N}. We prove that the number of resonances counted with multiplicities and lying inside the disc of radius R behaves asymptotically linear W-X is an element of R + O(1) as R -> infinity, where the constant W-X is an element of[0, V-X] can be seen as the effective size of X. Moreover, we show that there exist a configuration of any number of points such that W-X = V-X. Finally, we construct an example for N = 4 with W-X < V-X, which can be viewed as an analogue of a quantum graph with non-Weyl asymptotics of resonances.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10306 - Optics (including laser optics and quantum optics)

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

Acta Physica Polonica. A

ISSN

0587-4246

e-ISSN

—

Svazek periodika

132

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

6

Strana od-do

1677-1682

Kód UT WoS článku

000418702900006

EID výsledku v databázi Scopus

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