On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$

Emanuela L. Giacomelli

On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$

Analysis of PDEs 2022-07-29 v1 Spectral Theory

Authors: Emanuela L. Giacomelli

Abstract

We consider the Neumann realization of the magnetic laplacian in $\mathbb{R}^3_+$ , in the case in which the magnetic field has a piecewise constant strength and a uniform direction. This operator is expected to be an effective model in studying the threshold to the normal state for a 3D superconductor exposed to a discontinuous magnetic field. We review some recent results above the infimum of the spectrum of the aforementioned operator.

Keywords

magnetic laplacian neumann realization piecewise constant magnetic field superconductor spectrum r3+

Cite

@article{arxiv.2207.13627,
  title  = {On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$},
  author = {Emanuela L. Giacomelli},
  journal= {arXiv preprint arXiv:2207.13627},
  year   = {2022}
}

Comments

11 pages, contribution to the Proceedings of the Intensive Period "INdAM Quantum Meetings (IQM22)" at Politecnico di Milano, March - May 2022

On the magnetic laplacian with a piecewise constant magnetic field in $\mathbb{R}^3_+$

Abstract

Keywords

Cite

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