• Corpus ID: 247922836

A 3D-Schroedinger operator under magnetic steps

@inproceedings{Assaad2021A3O,
  title={A 3D-Schroedinger operator under magnetic steps},
  author={W. Assaad and Emanuela L Giacomelli},
  year={2021}
}
. We define a Schrödinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the spectrum of the operator. We further give sufficient conditions on the strength and the direction of the magnetic field such that the aforementioned infimum is an eigenvalue of a reduced model operator on the half-plane. 
View PDF on arXiv

Figures from this paper

References

SHOWING 1-10 OF 44 REFERENCES
The model magnetic Laplacian on wedges
We study a model Schrodinger 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…
The Schrödinger operator on an infinite wedge with a tangent magnetic field
We study a model Schrodinger 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…
The Distribution of Superconductivity Near a Magnetic Barrier
We consider the Ginzburg–Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a…
Lowest energy band function for magnetic steps
We study the Schrödinger operator in the plane with a step magnetic field function. The bottom of its spectrum is described by the infimum of the lowest eigenvalue band function, for which we…
Remarks on the spectrum of the Neumann problem with magnetic field in the half-space
We consider a Schrodinger operator with a constant magnetic field in a one-half three-dimensional space, with Neumann-type boundary conditions. It is known from the works by Lu–Pan and Helffer–Morame…
Eigenvalue problems of Ginzburg–Landau operator in bounded domains
In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in R2 under gauge invariant boundary conditions. The estimates for the…
On the Third Critical Field in Ginzburg-Landau Theory
AbstractUsing recent results by the authors on the spectral asymptotics of the Neumann Laplacian with magnetic field, we give precise estimates on the critical field, $$H_{C_3}$$, describing the…
Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)
. 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 non-uniform…
From the Laplacian with variable magnetic field to the electric Laplacian in the semiclassical limit
We consider a twisted magnetic Laplacian with Neumann condition on a smooth and bounded domain of $\R^2$ in the semiclassical limit $h\to 0$. Under generic assumptions, we prove that the eigenvalues…
Schrodinger Operators: With Application to Quantum Mechanics and Global Geometry
Self-Adjointness.- Lp-Properties of Eigenfunctions, and All That.- Geometric Methods for Bound States.- Local Commutator Estimates.- Phase Space Analysis of Scattering.- Magnetic Fields.- Electric…
...
...