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pro vyhledávání: '"GOLENIA, Sylvain"'
Limiting absorption principle for long-range perturbation in the discrete triangular lattice setting
We study the discrete Laplacian acting on a triangular lattice. We perturb the metric and the potential in a long-range way. We aim at proving a Limiting Absorption Principle away the possible embedded eigenvalues. The approach is based on a positive
Externí odkaz:
http://arxiv.org/abs/2403.06578
Autor:
Golénia, Sylvain, Mandich, Marc-Adrien
This document contains additional numerical and graphical evidence to support some of the conjectures mentioned in \cite{GM3}. We give more evidence for $\kappa=3,4$ in dimension 2. As mentioned in that article we still don't quite understand the set
Externí odkaz:
http://arxiv.org/abs/2201.09547
Autor:
Golénia, Sylvain, Mandich, Marc-Adrien
We continue the investigation of the existence of absolutely continuous (a.c.) spectrum for the discrete Schr\"odinger operator $\Delta+V$ on $\ell^2(\Z^d)$, in dimensions $d\geq 2$, for potentials $V$ satisfying the long range condition $n_i(V-\tau_
Externí odkaz:
http://arxiv.org/abs/2201.09545
We study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schr{\"o}dinger operators on these graphs. We obtain estimates on the first and second order term of the eigenvalue asymptotics. Moreover, we prov
Externí odkaz:
http://arxiv.org/abs/2104.03582
Autor:
Golenia, Sylvain, Mandich, Marc Adrien
Commutator methods are applied to get limiting absorption principles for the discrete standard and Molchanov-Vainberg Schr\"odinger operators $H_{\mathrm{std}}= \Delta+V$ and $H_{\mathrm{MV}} = D+V$ on $\ell^2(\mathbb{Z}^d)$, with emphasis on $d=1,2,
Externí odkaz:
http://arxiv.org/abs/2102.00726
Autor:
Golenia, Sylvain, Truc, Françoise
In 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schr{\"o}dinger operator with the help of some localisations at infinity. A key hypothesis is that the distance between two consecutive bump
Externí odkaz:
http://arxiv.org/abs/2003.11792
Autor:
Golenia, Sylvain, Mandich, Marc-Adrien
Publikováno v:
Annales Henri Poincar{\'e}, Springer Verlag, 2021, 22 (1), pp.83-120
We consider discrete Schr{\"o}dinger operators on ${\mathbb{Z}}^d$ for which the perturbation consists of the sum of a long-range type potential and a Wigner-von Neumann type potential. Still working in a framework of weighted Mourre theory, we impro
Externí odkaz:
http://arxiv.org/abs/2002.04909
We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from the p
Externí odkaz:
http://arxiv.org/abs/1902.04467
We study magnetic Schr\"odinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnetic sparse turn out to be equivalent to the fact that the form domain
Externí odkaz:
http://arxiv.org/abs/1711.10418
Autor:
Golenia, Sylvain, Mandich, Marc-Adrien
Publikováno v:
Integr. Equ. Oper. Theory (2018) 90:47
In the abstract framework of Mourre theory, the propagation of states is understood in terms of a conjugate operator $A$. A powerful estimate has long been known for Hamiltonians having a good regularity with respect to $A$ thanks to the limiting abs
Externí odkaz:
http://arxiv.org/abs/1703.08042