Related papers: Effective operators on an attractive magnetic edge
In the paper some regimes of motion of an electric dipole placed in a uniform magnetic field are considered. The motion of both three-dimensional and two-dimensional dipole in the plane perpendicular to the magnetic field is studied. In 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 use the perturbative method to study the influence of the magnetic field on the weak deflection angle of charged signals in magnetized stationary and axisymmetric spacetimes within general electromagnetic potentials. The deflection angle…
The reduction of the three-dimensional classical electromagnetism is performed in a twofold way. In the first case the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing…
We present a semiclassical theory for electron drag between two parallel two-dimensional electron systems in a strong magnetic field, which provides a transparent picture of the most salient qualitative features of anomalous drag phenomena…
This paper concerns the shape optimization problem of minimizing the ground state energy of the magnetic Dirichlet Laplacian with constant magnetic field among three-dimensional domains of fixed volume. In contrast to the two-dimensional…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…
We define a Schr\"odinger 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 superconductivity, we study the infimum of the…
We study functional and spectral properties of perturbations of the magnetic Laplace operator on the circle. This operator appears when considering the restriction to the unit circle of a two-dimensional Schr{\"o}dinger operator with the…
The core result of this paper is an upper bound for the ground state energyof the magnetic Laplacian with constant magnetic field on cones that are contained in ahalf-space. This bound involves a weighted norm of the magnetic field related…
Double forms are sections of the vector bundles $\Lambda^{k}T^*\mathcal{M}\otimes \Lambda^{m}T^*\mathcal{M}$, where in this work $(\mathcal{M},\mathfrak{g})$ is a compact Riemannian manifold with boundary. We study graded second-order…
On a closed hyperbolic surface, we investigate semiclassical defect measures associated with the magnetic Laplacian in the presence of a constant magnetic field. Depending on the energy level where the eigenfunctions concentrate, three…
In this note we consider the Iwatsuka model with a postive increasing magnetic field having finite limits. The associated magnetic Laplacian is fibred through partial Fourier transform, and, for large frequencies, the band functions tend to…
We consider a magnetic laplacian P(A) on the Poincar\'e half-plane, when the magnetic field dA is infinite at infinity such that P(A) has pure discret spectrum. We give the asymptotic behavior of the counting function of the eigenvalues.
Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map…
We define the random magnetic Laplacien with spatial white noise as magnetic field on the two-dimensional torus using paracontrolled calculus. It yields a random self-adjoint operator with pure point spectrum and domain a random subspace of…
We complete the analysis of the band functions for two-dimensional magnetic Schr\"odinger operators with piecewise constant magnetic fields. The discontinuity of the magnetic field can create edge currents that ow along the discontinuity…
It is shown that the dynamics of the growth of a two dimensional surface in a Laplacian field can be mapped onto Hamiltonian dynamics. The mapping is carried out in two stages: first the surface is conformally mapped onto the unit circle,…
The magnetic dipole (M1) and electric quadupole (E2) responses of two-dimensional quantum dots with an elliptic shape are theoretically investigated as a function of the dot deformation and applied static magnetic field. Neglecting the…
We consider Laplacians on periodic metric graphs with unit-length edges. The spectrum of these operators consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite…