Related papers: Magnetic Wells in Dimension Three

In terms of the matrix valued Berry gauge field strength for the Weyl Hamiltonian in any even spacetime dimensions a symplectic form whose elements are matrices in spin indices is introduced. Definition of the volume form is modified…

We consider a relativistic no-pair model of a hydrogenic atom in a classical, exterior magnetic field. First, we prove that the corresponding Hamiltonian is semi-bounded below, for all coupling constants less than or equal to the critical…

We design sub-wavelength high-performing non-reciprocal optical devices using recently discovered magnetic Weyl semimetals. These passive bulk topological materials exhibit anomalous Hall effect which results in magnetooptical effects that…

We show that the appropriate notion of magnetic field on three-dimensional contact sub-Riemannian manifolds is given by a closed Rumin differential two-form. We introduce horizontal magnetic flows starting from magnetic potential one-forms,…

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is…

In this paper, we examine eigenfunctions of a generalized Landau Magnetic Laplacian that models the physics of an electron confined to a plane in a magnetic field orthogonal to the plane. This operator has an infinite dimensional null space…

We study asymptotical behaviour of resonances for a quantum graph consisting of a finite internal part and external leads placed into a magnetic field, in particular, the question whether their number follows the Weyl law. We prove that the…

We consider the magnetic Dirichlet Laplacian with constant magnetic field on domains of finite measure. First, in the case of a disk, we prove that the eigenvalue branches with respect to the field strength behave asymptotically linear with…

Weyl fermions, which are fermions with definite chiralities, can give rise to anomalous breaking of the symmetry of the physical system which they are a part of. In their (3+1)-dimensional realizations in condensed matter systems, i.e., the…

In this paper we study in detail some spectral properties of the magnetic discrete Laplacian. We identify its form-domain, characterize the absence of essential spectrum and provide the asymptotic eigenvalue distribution.

Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to infinity as the magnetic field tends to infinity.…

This paper is devoted to the semiclassical magnetic Laplacian. Until now WKB expansions for the eigenfunctions were only established in presence of a non-zero electric potential. Here we tackle the pure magnetic case. Thanks to…

We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let $B$ be the strength of the magnetic field, and let $\lambda_1(B)$ be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved…

We consider the semi-classical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm-Kova\v{r}\'ik-Portmann and Helffer-Sundqvist for the asymptotics of…

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture $\alpha$ and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular,…

We study the energy spectrum of a two-dimensional electron in the presence of both a perpendicular magnetic field and a potential. In the limit where the potential is small compared to the Landau level spacing, we show that the broadening…

We study the asymptotic behavior, as Planck's constant $\hbar\to 0$, of the number of discrete eigenvalues and the Riesz means of Pauli and Dirac operators with a magnetic field $\mu\mathbf{B}(x)$ and an electric field. The magnetic field…

On a suitable class of non-compact manifolds, we study (pseudo)differential operators which feature an asymptotic translation-invariance along one axis and an asymptotic dilation-invariance, or asymptotic homogeneity with respect to…

In this paper we derive formulae for the semiclassical tunneling in the presence of a constant magnetic field in 2 dimensions. The `wells' in the problem are identical discs with Neumann boundary conditions, so we study the magnetic Neumann…

We propose that Weyl triplons are expected to appear in the low energy magnetic excitations in the canonical Shastry-Sutherland compound, \ce{SrCu2(BO3)2}, a quasi-2D quantum magnet. Our results show that when a minimal, realistic…