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The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the…
We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schr\"odinger operator with an attractive $\delta$-interaction of a fixed strength, the support of which is a star graph with finitely many…
We study the asymptotic distribution of the resonances near the Landau levels $\Lambda\_q =(2q+1)b$, $q \in \mathbb{N}$, of the Dirichlet (resp. Neumann, resp. Robin) realization in the exterior of a compact domain of $\mathbb{R}^3$ of the…
For a Schr\"odinger operator on the plane $\mathbb{R}^2$ with electric potential $V$ and Aharonov--Bohm magnetic field we obtain an upper bound on the number of its negative eigenvalues in terms of the $L^1(\mathbb{R}^2)$-norm of $V$.…
We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (-Delta)^{alpha/2} in the unit ball D in R^d, with a Dirichlet condition in the complement of D. The…
We show that the third eigenvalue of the Neumann Laplacian in hyperbolic space is maximal for the disjoint union of two geodesic balls, among domains of given volume. This extends a recent result by Bucur and Henrot in Euclidean space,…
We derive an expression for the macroscopic force density that a narrow-band electromagnetic field imposes on a dissipative isotropic medium. The result is obtained by averaging the microscopic form for Lorentz force density. The derived…
In this paper we study local stability estimates for a magnetic Schr\"odinger operator with partial data on an open bounded set in dimension $n\geq 3$. This is the corresponding stability estimates for the identifiability result obtained by…
We study the minimizers of the Ginzburg-Landau energy functional with a constant magnetic field in a three dimensional bounded domain. The functional depends on two positive parameters, the Ginzburg-Landau parameter and the intensity of the…
Single crystals of Nd$_2$O$_3$ were grown and characterized using neutron scattering and thermodynamic measurements. Nd$_2$O$_3$ has long-range antiferromagnetic order below $T_{\rm N}$ = 0.55 K and specific heat measurements have…
We derive the exact solution of the Boltzmann kinetic equation for the three-dimensional Lorentz model in the presence of a constant and uniform magnetic field. The velocity distribution of the electrons reduces exponentially fast to its…
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…
We study the large field limit in Schr\"odinger equations with magnetic vector potentials describing translationally invariant $B$-fields with respect to the $z$-axis. In a first step, using regular perturbation theory, we derive an…
We initiate the study of non- and ultra-relativistic higher spin theories. For sake of simplicity we focus on the spin-3 case in three dimensions. We classify all kinematical algebras that can be obtained by all possible In\"on\"u--Wigner…
In this article, we investigate the rate at which the first Dirichlet eigenvalue of geodesic balls decreases as the radius approaches infinity. We prove that if the conformal infinity of an asymptotically hyperbolic Einstein manifold is of…
Motivated by establishing Neumann Talenti type comparison results, we concern the minimization of the following shape functional under volume constraint: \begin{align*} T(\Omega):=\inf\left\{\frac12 \int_{\Omega} |\nabla u|^2\,dx…
We consider a magnetic Schr\"odinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well…
Consider the Coulomb potential $-\mu\ast|x|^{-1}$ generated by a non-negative finite measure $\mu$. It is well known that the lowest eigenvalue of the corresponding Schr\"odinger operator $-\Delta/2-\mu\ast|x|^{-1}$ is minimized, at fixed…
We study orbital magnetism in a three-dimensional (3D) quantum dot with a parabolic confining potential. We calculate the free energy of the system as a function of the magnetic field and the temperature. By this, we show that the…
We consider the asymptotic behavior of the spectrum of the Landau Hamiltonian plus a rapidly decaying potential, as the magnetic field strength, $B$, tends to infinity. After a suitable rescaling, this becomes a semiclassical problem where…