Related papers: Magnetic Laplacian in sharp three dimensional cone…
This paper is mainly inspired by the conjecture about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture $\phi\in (0,\pi)$. So far, a proof was only obtained for apertures $\phi\lesssim 0.511\pi$.…
The energy spectrum of an electron confined to an arbitrary surface of revolution in an external magnetic field, parallel to the symmetry axis, is studied analitycally and numerically. The problem is reduced via conformal mapping to one on…
We consider a magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ on a noncompact hyperbolic surface $\mM $ with finite area. $A$ is a real one-form and the magnetic field $dA$ is constant in each cusp. When the harmonic component of $A$…
We analyze the properties of magnons in metallic electron systems with spiral magnetic order. Our analysis is based on the random phase approximation for the susceptibilities of tight binding electrons with a local Hubbard interaction in…
The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3…
We study the 3D Neuman magnetic Laplacian in the presence of a semi-classical parameter and a non-uniform magnetic field with constant intensity. We determine a sharp two term asymptotics for the lowest eigenvalue, where the second term…
On a closed, orientable Riemannian surface $\Sigma_g$ of arbitrary genus $g\geq 1$ and Riemannian metric $h$ we study the magnetic Laplacian with magnetic potential given by a harmonic $1$-form $A$. Its lowest eigenvalue (magnetic ground…
On the basis of analytic solutions of Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential the equations for the bound one-active electron states are discussed. It is vary…
For certain compactly supported metric and/or potential perturbations of the Laplacian on $\mathbb{H}^{n+1}$, we establish an upper bound on the resonance counting function with an explicit constant that depends only on the dimension, the…
The ground state properties of the Shastry-Sutherland model in the presence of an external field are investigated by means of variational states built up from unpaired spins (monomers) and singlet pairs of spins (dimers). The minimum of the…
An approximate analytic solution for the ground electron state are found to the Schroedinger equation for a combination of a uniform magnetic field and single attractive delta-potential. Effect of the magnetic field on this bound localized…
Relative magnetic helicity is commonly used in solar physics to avoid the well known gauge ambiguity of standard magnetic helicity in magnetically open domains. But its physical interpretation is difficult owing to the invocation of a…
The bound state in the system of three protons and an electron (pppe) under a homogeneous strong magnetic field where the protons are situated in the vertices of an equilateral triangle perpendicular to the magnetic field lines is found. It…
It is well known that the spectrum of the Dirichlet Laplacian for a compact perturbation of a three-dimensional, periodically twisted tube is unstable with respect to domain deformations. This means that if the periodically twisted tube is…
In three-dimensional space an electron moving in the field of a magnetic monopole has no bound states. In this paper we explore the physics when the electron is restricted to a two-dimensional plane adjacent to a magnetic monopole. We find…
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…
We derive a bound on the magnetic dipole moment of the top quark in the context of the effective Lagrangian approach by using the values of the ratio $R_b = \Gamma_b/\Gamma_h$, $R_l = \Gamma_h/\Gamma_l$ and $\Gamma_Z$. We found that the…
Type-II superconductivity is known to persist close to the sample surface in presence of a strong magnetic field. As a consequence, the ground state energy in the Ginzburg-Landau theory is approximated by an effective one-dimensional model.…
The magnetic Laplacian on hyperbolic surfaces provides a rich analytic framework in which a variety of quantum phenomena emerge. The present note, written for the \emph{Proceedings of the Journ\'ees EDP 2025}, is a concise overview of the…
We estimate the magnetic Laplacian energy norm in appropriate planar domains under a weak regularity hypothesis on the magnetic field. Our main contribution is an averaging estimate, valid in small cells, allowing us to pass from…