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pro vyhledávání: '"47A40"'
We prove a Rellich-Vekua type theorem for Schr\"{o}dinger operators with exponentially decreasing potentials on a class of lattices containing square, triangular, hexagonal lattices and their ladders. We also discuss the unique continuation theorem a
Externí odkaz:
http://arxiv.org/abs/2411.03577
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
Autor:
Fermi, Davide
This work provides an introduction and overview on some basic mathematical aspects of the single-flux Aharonov-Bohm Schr\"odinger operator. The whole family of admissible self-adjoint realizations is characterized by means of four different methods:
Externí odkaz:
http://arxiv.org/abs/2407.15115
We introduce a family of Helson matrices induced by the Laplace transform of a class of regular positive Borel measures $\mu,$ not necessarily finite, on $(0, \infty)$ and discuss their boundedness, Schatten-class properties and scattering theory. We
Externí odkaz:
http://arxiv.org/abs/2407.04124
Autor:
Alexander, Angus, Rennie, Adam
We use spectral flow to present a new proof of Levinson's theorem for Schr\"{o}dinger operators on $\mathbb{R}^n$ with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The statement is expr
Externí odkaz:
http://arxiv.org/abs/2405.19571
Autor:
Taira, Kouichi
A local time decay estimate of fractional Schr\"odinger operators with slowly decaying positive potentials are studied. It is shown that its resolvent is smooth near zero and the time propagator has fast local time decay which is very different from
Externí odkaz:
http://arxiv.org/abs/2403.16148
Autor:
Alexander, Angus
We realise the number of bound states of a Schr\"{o}dinger operator on $\mathbb{R}^n$ as an index pairing in all dimensions. Expanding on ideas of Guillop\'{e} and others, we use high-energy corrections to find representatives of the $K$-theory class
Externí odkaz:
http://arxiv.org/abs/2402.15979
This paper is dedicated to the introduction in a circle of ideas and methods, which are connected with the notion of characteristic function of a non-selfadjoint operator. We start with the consideration of closed and open systems (Subsections 2.1.1-
Externí odkaz:
http://arxiv.org/abs/2312.17333
Autor:
Boiko, Sergey S., Dubovoy, Vladimir K., Fritzsche, Bernd, Kirstein, Bernd, Mädler, Conrad, Müller, Karsten
In this paper we would like to show the interrelation between the different mathematical theories concerning the Schur interpolation problem, contractions in Hilbert spaces, pseudocontinuation and Darlington synthesis. The main objects of this articl
Externí odkaz:
http://arxiv.org/abs/2312.17177
Publikováno v:
J. Spectral Theory 14(3), 1147-1193 (2024)
We study a two-dimensional Pauli operator describing a charged quantum particle with spin $1/2$ moving on a plane in presence of an orthogonal Aharonov-Bohm magnetic flux. We classify all the admissible self-adjont realizations and give a complete pi
Externí odkaz:
http://arxiv.org/abs/2312.11971