Related papers: The Laplacian with complex magnetic fields
We show that in perfectly quasi-isodynamic magnetic fields, which are generally non-quasisymmetric and which can approximate fields of experimental interest, neoclassical calculations can be carried out analytically more completely than in…
We consider a magnetic Laplacian on a geometrically finite hyperbolic surface, when the corresponding magnetic field is infinite at the boundary at infinity. We prove that the counting function of the eigenvalues has a particular asymptotic…
This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. Boundary conditions are…
Gauge field configuration for a magnetic monopole and its dual configuration are studied in SU(2) gauge theory. We present a relation between the monopole field and its dual field. Since these fields can become massive, their massive…
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the 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…
We study perturbations of the discrete magnetic Laplacian associated to discrete analogs of funnels. We perturb the metric in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from possible…
This paper presents a quantum field theoretical formalism for studying magnons in finite nanostructures with arbitrary shapes and spatially nonuniform ground states. It extends the classical micromagnetic formalism by introducing a…
In dimensions d= 1, 2, 3 the Laplacian can be perturbed by a point potential. In higher dimensions the Laplacian with a point potential cannot be defined as a self-adjoint operator. However, for any dimension there exists a natural family…
A bounded domain in several complex variables with connected Lipschitz boundary is pseudoconvex if and only if the bottom of the (essential) spectrum of the Kohn Laplacian is positive on all (0, q)-forms with square-integrable coefficients.
A multi-band effective-mass Hamiltonian is derived for lattice-matched semiconductor nanostructures in a slowly varying external magnetic field. The theory is derived from the first-principles magnetic-field coupling Hamiltonian of Pickard…
The analysis of the dynamics of a material point perfectly constrained to a submanifold of the three-dimensional euclidean space and subjected to a locally conservative force's field, namely a force's field corresponding to a closed but not…
We develop the basic formalism of complex $q$-analysis to study the solutions of second order $q$-difference equations which reduce, in the $q\rightarrow 1$ limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After…
This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…
In accordance with the Keller-Maslov global WKB theory, a semiclassical scalar wave field is best encoded as a triple consisting of (i) a Lagrangian submanifold $\Lambda$ in the ray phase space, (ii) a density $\mu$ on $\Lambda$, and (iii)…
Cosmological magnetic fields in open Friedmann universes can experience superadiabatic amplification within the realm of conventional electromagnetism. This is possible mathematically, despite the conformal invariance of Maxwell's…
We investigate the question discussed in the literature as to whether the magnetic field can perform work using two models that describe interacting magnetic dipoles. In the first model, the dipoles are realized by rigidly rotating charge…
This paper is devoted to the study of the two-dimensional Dirac-Coulomb operator in presence of an Aharonov-Bohm external magnetic potential. We characterize the highest intensity of the magnetic field for which a two-dimensional magnetic…
The aim of the paper is to derive spectral estimates on the eigenvalue moments of the magnetic Dirichlet Laplacian defined on the two-dimensional disk with a radially symmetric magnetic field.
We study the Laplacian with zero magnetic field acting on complex functions of a planar domain $\Omega$, with magnetic Neumann boundary conditions. If $\Omega$ is simply connected then the spectrum reduces to the spectrum of the usual…