arXiv subjects

Nicolas Popoff

Publications and source records attributed to Nicolas Popoff.

22 records · Page 2Linked to original sources

arXiv2014

The Schrödinger operator on an infinite wedge with a tangent magnetic field

We study a model Schrödinger operator with constant magnetic field on an infinite wedge with Neumann boundary condition. The magnetic field is assumed to be tangent to a face. We compare the bottom of the spectrum to the model spectral quantities coming from the regular case. We are particularly motivated by the influence of the magnetic field and the opening angle of the wedge on the spectrum of the model operator and we exhibit cases where the bottom of the spectrum is smaller than in the regular case. Numerical computations enlighten the theoretical approach.

math.AP↗

arXiv2013

Ground Energy of the Magnetic Laplacian in Polyhedral Bodies

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the model problems (continuity, semi-continuity, existence of generalized eigenfunctions). We prove estimates for the remainders of our asymptotic formula. Lower bounds are obtained with the help of a classical IMS partition based on adequate coverings of the polyhedral domain, whereas upper bounds are established by a novel construction of quasimodes, qualified as sitting or sliding according to spectral properties of local model problems.

math.AP↗

arXiv2013

The model magnetic Laplacian on wedges

We study a model Schrödinger operator with constan tmagnetic field on an infinite wedge with natural boundary conditions. This problem is related to the semiclassical magnetic Laplacian on 3d domains with edges. We show that the ground energy is lower than the one coming from the regular part of the wedge and is continuous with respect to the geometry. We provide an upper bound for the ground energy on wedges of small opening. Numerical computations enlighten the theoretical approach.

math.AP↗

arXiv2013

On the lowest energy of a 3D magnetic hamiltonian with axisymmetric potential

We study the bottom of the spectrum of a magnetic hamiltonian with axisymmetrical potential in R3. The associated magnetic field is planar, unitary and non-constant. The problem reduces to a 1D-family of singular Sturm-Liouville operators on the half-line. We study to associated band functions and we compare it to the "de Gennes" operators arising in the study of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field. We show in particular that the lowest energy is higher in dimension 3.

math.SP↗