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pro vyhledávání: '"Point interactions"'
Autor:
Noja, Diego, Scandone, Raffaele
We consider Schr\"odinger operators on a bounded domain $\Omega\subset \mathbb{R}^3$, with homogeneous Robin or Dirichlet boundary conditions on $\partial\Omega$ and a point (zero-range) interaction placed at an interior point of $\Omega$. We show th
Externí odkaz:
http://arxiv.org/abs/2412.16056
Autor:
Noja, Diego, Stoia, Francesco Raso
In this paper we describe the resonances of the singular perturbation of the Laplacian on the half space $\Omega =\mathbb R^3_+$ given by the self-adjoint operator named $\delta$-interaction or point interaction. We will assume Dirichlet or Neumann b
Externí odkaz:
http://arxiv.org/abs/2410.12998
We determine the principal term of the asymptotics of the integrated density of states (IDS) $N(\lambda)$ for the Schr\"odinger operator with point interactions on $\mathbf{R}^3$ as $\lambda \to -\infty$, provided that the set of positions of the poi
Externí odkaz:
http://arxiv.org/abs/2406.02256
We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave packets)
Externí odkaz:
http://arxiv.org/abs/2407.15521
Autor:
Moscato, Antonio
This paper shows that the resolvent algebra $\mathcal{R}\left( \mathbb{R}^2,\sigma \right)$ can accommodate dynamics induced by self-adjoint Hamiltonians on $L^2\left( \mathbb{R} \right)$ describing a single non-relativistic spinless particle undergo
Externí odkaz:
http://arxiv.org/abs/2401.09357
Publikováno v:
J. Phys.: Conf. Ser. 2667 012071 (2023)
First we recall a method of computing scalar products of eigenfunctions of a Sturm-Liouville operator. This method is then applied to Macdonald and Gegenbauer functions, which are eigenfunctions of the Bessel, resp. Gegenbauer operators. The computed
Externí odkaz:
http://arxiv.org/abs/2311.03135
The spectrum of a one-dimensional pseudospin-one Hamiltonian with a three-component potential is studied for two configurations: (i) all the potential components are constants over the whole coordinate space and (ii) the profile of some components is
Externí odkaz:
http://arxiv.org/abs/2310.17934
Akademický článek
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We investigate the entire family of multi-center point interaction Hamiltonians. We show that a large sub-family of these operators do not become either singular or trivial when the positions of two or more scattering centers tend to coincide. In thi
Externí odkaz:
http://arxiv.org/abs/2306.10292
Autor:
Budyka, V. S.1 (AUTHOR) budyka.vik@gmail.com, Malamud, M. M.2,3 (AUTHOR), Pokrovskii, I. L.4 (AUTHOR)
Publikováno v:
Mathematical Notes. Dec2023, Vol. 114 Issue 5/6, p1060-1066. 7p.
