Asymptotics of Resonances Induced by Point Interactions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F17%3A50013949" target="_blank" >RIV/62690094:18470/17:50013949 - isvavai.cz</a>
Result on the web
<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>

Result language
angličtina
Original language name
Asymptotics of Resonances Induced by Point Interactions
Original language description
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) |x(n) - x(pi(n))|, 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/pi*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.
Czech name
—
Czech description
—

Project
<a href="/en/project/GJ15-14180Y" target="_blank" >GJ15-14180Y: Spectral and resonance properties of quantum models</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

Article name in the collection
Acta physica polonica. Seria A, General physics, solid state physics, applied physics
ISBN
—
ISSN
0587-4246
e-ISSN
neuvedeno
Number of pages
6
Pages from-to
1677-1682
Publisher name
Panstwowe wydawnictvo naukowe
Place of publication
Warszawa
Event location
Warsaw
Event date
May 19, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000418702900006

Similar results(10)