- Tytuł:
- Asymptotics of Resonances Induced by Point Interactions
- Autorzy:
-
Lipovský, J.
Lotoreichik, V. - Powiązania:
- https://bibliotekanauki.pl/articles/1030012.pdf
- Data publikacji:
- 2017-12
- Wydawca:
- Polska Akademia Nauk. Instytut Fizyki PAN
- Tematy:
-
03.65.Ge
03.65.Nk
02.10.Ox - Opis:
- We consider the resonances of the self-adjoint three-dimensional Schrödinger operator with point interactions of constant strength supported on the set X={xₙ}_{n=1}^{N}. The size of X is defined by V_{X} = max_{π ∈ Π_{N}} ∑_{n=1}^{N} |xₙ - x_{π(n)}|, where Π_{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}/πR + O(1) as R → ∞, where the constant W_{X} ∈ [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.
- Źródło:
-
Acta Physica Polonica A; 2017, 132, 6; 1677-1682
0587-4246
1898-794X - Pojawia się w:
- Acta Physica Polonica A
- Dostawca treści:
- Biblioteka Nauki
Artykuł