# Lowest energy band function for magnetic steps

@inproceedings{Assaad2020LowestEB, title={Lowest energy band function for magnetic steps}, author={W. Assaad and Ayman Kachmar}, year={2020} }

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 establish the existence and uniqueness of the non-degenerate minimum. We discuss the curvature effects on the localization properties of magnetic ground states, among other applications.

## 6 Citations

A 3D-Schroedinger operator under magnetic steps

- Mathematics
- 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…

Effective operators on an attractive magnetic edge

- Mathematics, Physics
- 2022

. The semiclassical Laplacian with discontinuous magnetic ﬁeld is considered in two dimensions. The magnetic ﬁeld is sign changing with exactly two distinct values and is discontinuous along a smooth…

Magnetic quantum currents in the presence of a Neumann wall

- Mathematics
- 2022

We consider the Schrödinger operator with constant transverse magnetic field on a half-plane, endowed with Neumann boundary conditions. We study the low energy currents flowing along the boundary and…

Tunneling effect induced by a curved magnetic edge

- Physics
- 2022

Experimentally observed magnetic fields with nanoscale variations are theoretically modeled by a piece-wise constant function with jump discontinuity along a smooth curve, the magnetic edge. Assuming…

Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)

- Mathematics
- 2021

. 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…

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

- Mathematics, Physics
- 2022

We consider the Neumann realization of the magnetic laplacian in R 3+ , in the case in which the magnetic ﬁeld has a piecewise constant strength and a uniform direction. This operator is expected to…

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