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- W2963275556 abstract "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 $V_X = max_{piinPi_N} sum_{n=1}^N |x_n - x_{pi(n)}|$, where $Pi_N$ is the family of all the permutations of the set ${1,2,dots,N}$. We prove that the number of resonances counted with multiplicities and lying inside the disc of radius $R$ behaves asymptotically linear $frac{W_X}{pi} R + mathcal{O}(1)$ as $R to infty$, where the constant $W_X in [0,V_X]$ can be seen as the effective size of $X$. Moreover, we show that there exist configurations 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." @default.
- W2963275556 created "2019-07-30" @default.
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- W2963275556 date "2017-12-01" @default.
- W2963275556 modified "2023-09-28" @default.
- W2963275556 title "Asymptotics of Resonances Induced by Point Interactions" @default.
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- W2963275556 doi "https://doi.org/10.12693/aphyspola.132.1677" @default.
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