The model magnetic Laplacian on wedges

@article{Popoff2013TheMM,
  title={The model magnetic Laplacian on wedges},
  author={Nicolas Popoff},
  journal={arXiv: Analysis of PDEs},
  year={2013}
}
  • N. Popoff
  • Published 24 September 2013
  • Mathematics
  • arXiv: Analysis of PDEs
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 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. 
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12 Citations
Background Citations
5
Methods Citations
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12 Citations

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References

SHOWING 1-10 OF 59 REFERENCES
On the semi-classical 3D Neumann Laplacian with variable magnetic field
In this paper we are interested in the semi-classical estimates of the spectrum of the Neumann Laplacian in dimension 3. This work aims to present a complementary case to the one presented in the…
Discrete spectrum of a model Schrödinger operator on the half-plane with Neumann conditions
We study the eigenpairs of a model Schrödinger operator with a quadratic potential and Neumann boundary conditions on a half-plane. The potential is degenerate in the sense that it reaches its…
LOCATING THE SPECTRUM FOR MAGNETIC SCHRöDINGER AND DIRAC OPERATORS
ABSTRACT Some spectral properties of magnetic Schrödinger and Dirac operators perturbed by long range magnetic fields are investigated. If the intensity of the field is small enough, a better…
Asymptotics for the Low-Lying Eigenstates of the Schrödinger Operator with Magnetic Field near Corners
Abstract.The Neumann realization for the Schrödinger operator with magnetic field is considered in a bounded two-dimensional domain with corners. This operator is associated with a small…
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…
On the Lipschitz Continuity of Spectral Bands of Harper-Like and Magnetic Schrödinger Operators
We show for a large class of discrete Harper-like and continuous magnetic Schrödinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant…
On the fundamental state energy for a Schrödinger operator with magnetic field in domains with corners
The superconducting properties of a sample submitted to an external magnetic field are mathematically described by the minimizers of the Ginzburg-Landau’s functional. The analysis of the Hessian of…
Some Propagation Properties of the Iwatsuka Model
Abstract:In this paper we study a two dimensional magnetic field Schrödinger Hamiltonian introduced in [7]. This model has some interesting propagation properties, as conjectured in [2] and at the…
Magnetic bottles for the Neumann problem: The case of dimension 3
The main object of this paper is to analyze the recent results obtained on the Neumann realization of the Schrödinger operator in the case of dimension 3 by Lu and Pan. After presenting a short…
Magnetic bottles for the Neumann problem: curvature effects in the case of dimension 3
...
...