42 citations · 45 across the 6 of their papers we have counts for
8 papers
Spectral analysis of The magnetic Laplacian acting on discrete funnels
Nassim Athmouni, Marwa Ennaceur, Sylvain Golénia
We study perturbations of the discrete magnetic Laplacian associated to discrete analogs of funnels. We perturb the metric in a long-range way. We establish a propagation estimate…
Additional numerical and graphical evidence to support some Conjectures on discrete Schrödinger operators with a more general long range condition
Sylvain Golénia, Marc-Adrien Mandich
This document contains additional numerical and graphical evidence to support some of the conjectures mentioned in \cite{GM3}. We give more evidence for in dimension 2. As…
Thresholds and more bands of a.c. Spectrum for the discrete Schr{ö}dinger operator with a more general long range condition
Sylvain Golénia, Marc-Adrien Mandich
We continue the investigation of the existence of absolutely continuous (a.c.) spectrum for the discrete Schrödinger operator on , in dimensions , for…
The magnetic Laplacian acting on discrete cusps
Sylvain Golénia, Françoise Truc
We introduce the notion of discrete cusp for a weighted graph. In this context, we provethat the form-domain of the magnetic Laplacian and that of thenon-magnetic Laplacian can be…
The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs
Sylvain Golénia, Christoph Schumacher
The number of self-adjoint extensions of a symmetric operator acting on a complex Hilbert space is characterized by its deficiency indices. Given a locally finite unoriented simple…
Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians
Sylvain Golénia
We perform the spectral analysis of a zero temperature Pauli-Fierz system for small coupling constants. Under the hypothesis of Fermi golden rule, we show that the embedded eigenva…
The spectrum of Schrödinger operators and Hodge Laplacians on conformally cusp manifolds
Sylvain Golénia, Sergiu Moroianu
We describe the spectrum of the -form Laplacian on conformally cusp Riemannian manifolds. The essential spectrum is shown to vanish precisely when the and de Rham coho…
The spectrum of magnetic Schrödinger operators and -form Laplacians on conformally cusp manifolds
Sylvain Golénia, Sergiu Moroianu
We consider open manifolds which are interiors of a compact manifold with boundary, and Riemannian metrics asymptotic to a conformally cylindrical metric near the boundary. We show…