238 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Nantes UniversitéFR266 papers
- Centre National de la Recherche ScientifiqueFR187 papers
- Université de NantesFR152 papers
- École Centrale de NantesFR48 papers
- Laboratoire de Mathématiques d'OrsayFR36 papers
- Institut de recherche mathématique de RennesFR25 papers
- Institut FourierFR25 papers
- Université Paris-SudFR25 papers
- Université Paris-SaclayFR17 papers
- Institut national de recherche en sciences et technologies du numériqueFR12 papers
- Analyse, Géométrie et ModélisationFR11 papers
- Institut de Mathématiques de BordeauxFR11 papers
60 papers · 1 filter
The Spectral Shift Function for Non-Self-Adjoint Perturbations
Vincent Bruneau, Nicolas Frantz, François Nicoleau
This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by app…
On the Lebesgue Component of Semiclassical Measures for Abelian Quantum Actions
Gabriel Rivière, Lasse L. Wolf
For a large class of symplectic integer matrices, the action on the torus extends to a symplectic -action with . We apply this to the study of semiclassical…
Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains
Bernard Helffer, Ayman Kachmar, Francois Nicoleau
Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operato…
Tunneling effect in two dimensions with vanishing magnetic fields
Khaled Abou Alfa
In this paper, we consider the semiclassical 2D magnetic Schr{ö}dinger operator in the case where the magnetic field vanishes along a smooth closed curve. Assuming that this curve…
Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)
Wafaa Assaad, Bernard Helffer, Ayman Kachmar
We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues, for the Dirichlet magnetic Laplacian with a…
On the spectrum of some Bloch-Torrey vector operators
Yaniv Almog, Bernard Helffer
We consider the Bloch-Torrey operator in where . In contrast with the (as well as the $L^2({\mathbb R}^k,{\math…
Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field
Horia D. Cornean, Bernard Helffer, Radu Purice
This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two Bloch eigenvalues whi…
Spectrum of a non-selfadjoint quantum star graph
Gabriel Riviere, Julien Royer
We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Ro…
Large time behavior of solutions to Schrödinger equation with complex-valued potential
Maha Aafarani
We study the large-time behavior of the solutions to the Schrödinger equation associated with a quickly decaying potential in dimension three. We establish the resolvent expansions…
Semiclassical behaviour of quantum eigenstates
Gabriel Rivière
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We…
Separability and Symmetry Operators for Painlevé Metrics and their Conformal Deformations
Thierry Daudé, Niky Kamran, Francois Nicoleau
Painlevé metrics are a class of Riemannian metrics which generalize the well-known separable metrics of Stäckel to the case in which the additive separation of variables for the Ha…
Semiclassical asymptotics for nonselfadjoint harmonic oscillators
Victor Arnaiz, Gabriel Rivière
We consider nonselfadjoint perturbations of semiclassical harmonic oscillators. Under appropriate dynamical assumptions, we establish some spectral estimates such as upper bounds o…
Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator
Bernard Helffer, Qinghui Liu, Yanhui Qu +1
We show that there exists a dense set of frequencies with positive Hausdorff dimension for which the Hausdorff dimension of the spectrum of the critical almost Mathieu operator is…
The spectrum of a Schrödinger operator in a wire-like domain with a purely imaginary degenerate potential in the semiclassical limit
Yaniv Almog, Bernard Helffer
Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let denote an electric potential driven by a voltage drop between the conducting…
On the domain of a magnetic Schrödinger operator with complex electric potential
B Helffer, Jean Nourrigat
The aim of this paper is to review and compare the spectral properties of (the closed extension of) -- + U (V 0) and -- + iV in L 2 (R^d) for C real potentials…
Spectral semi-classical analysis of a complex Schrödinger operator in exterior domains
Yaniv Almog, Denis Grebenkov, Bernard Helffer
Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schrödinger operator with a purely imaginary potential $h…
Does Levinson's theorem count complex eigenvalues ?
F. Nicoleau, D. Parra, S. Richard
Yes it does ! Indeed an extended version of Levinson's theorem is proposed for a system involving complex eigenvalues. The perturbed system corresponds to a realization of the Schr…
Irregular time dependent perturbations of quantum Hamiltonians
Didier Robert
Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time dependent quantum Hamiltonians when this Hamiltonian is perturbed…
Non-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets
Thierry Daudé, Niky Kamran, Francois Nicoleau
In this paper, we give some simple counterexamples to uniqueness for the Calderon problem on Riemannian manifolds with boundary when the Dirichlet and Neumann data are measured on…
Mixed normal-superconducting states in the presence of strong electric currents
Yaniv Almog, Bernard Helffer, Xing-Bin Pan
We study the Ginzburg-Landau equations in the presence of large electric currents, that are smaller than the critical current where the normal state losses its stability. For stead…
Magnetic Wells in Dimension Three
Bernard Helffer, Yuri Kordyukov, Nicolas Raymond +1
This paper deals with semiclassical asymptotics of the three-dimensional magnetic Laplacian in presence of magnetic confinement. Using generic assumptions on the geometry of the co…
Local inverse scattering at a fixed energy for radial Schr{ö}dinger operators and localization of the Regge poles
Thierry Daudé, Francois Nicoleau
We study inverse scattering problems at a fixed energy for radial Schrödinger operators on , . First, we consider the class of potentials which…
Inverse scattering at fixed energy for massive charged Dirac fields in de Sitter-Reissner-Nordström black holes
Damien Gobin
In this paper, we consider massive charged Dirac fields propagating in the exterior region of de Sitter-Reissner-Nordström black holes.We show that the parameters of such black hol…
On the spectrum of non-selfadjoint Schrödinger operators with compact resolvent
Yaniv Almog, Bernard Helffer
We determine the Schatten class for the compact resolvent of Dirichlet realizations, in unbounded domains, of a class of non-selfadjoint differential operators. This class consists…