Related papers: Magnetic rings
We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are…
We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_\lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained…
We solved the Schr{\"o}dinger equation for a particle in a uniform magnetic field in the n-dimensional torus. We obtained a complete set of solutions for a broad class of problems; the torus T^n = R^n / {\Lambda} is defined as a quotient of…
We prove various equivalent characterisations of the Hardy space $H^p_{\mathcal{L}}(\mathbb{C}^n)$ for $0<p<1$ associated with the twisted Laplacian $\mathcal{L}$ which generalises the result of [MPR81] for the case $p=1$. Using the atomic…
This article deals with the uniqueness and stability issues in the inverse problem of determining the unbounded potential of the Schr\"odinger operator in a bounded domain of dimension 3 or greater, endowed with Robin boundary condition,…
This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…
We introduce a general class of long-range magnetic potentials and derive high velocity limits for the scattering operators in quantum mechanics, in the case of two dimensions. We analyze the high velocity limits in the presence of an…
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…
In this paper we deduce a formula for the fractional Laplace operator $(-\Delta)^{s}$ on radially symmetric functions useful for some applications. We give a criterion of subharmonicity associated with $(-\Delta)^{s}$, and apply it to a…
We establish inequalities for the eigenvalues of Schr\"odinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, complex and quaternionic projective spaces, which are related…
The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms, calls for systematic studies of orbital effects of the magnetic field…
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…
We consider the Schr\"odinger operator ${\bf H}=(i\nabla+A)^2 $ in the space $L_2({\mathbb R}^3)$ with a magnetic potential $A $ created by an infinite straight current. We perform a spectral analysis of the operator ${\bf H}$ almost…
We consider Schr\"odinger operators $H^h = (ih d+{\bf A})^* (ih d+{\bf A})$ with the periodic magnetic field ${\bf B}=d{\bf A}$ on covering spaces of compact manifolds. Under some assumptions on $\bf B$, we prove that there are arbitrarily…
We prove that a composition operator is bounded on the Hardy space $H^2$ of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative $\lambda$ there. In this case…
We consider the Schr\"odinger operators on zigzag nanoribbons (quasi-1D tight-binding models) in external magnetic fields and an electric potential $V$. The magnetic field is perpendicular to the plane of the ribbon and the electric field…
This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…
In this note we investigate three-dimensional Schr\"odinger operators with $\delta$-interactions supported on $C^2$-smooth cones, both finite and infinite. Our main results concern a Faber-Krahn-type inequality for the principal eigenvalue…
We prove Li-Yau-Kr\"oger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a…
We prove a simple sufficient criteria to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second-order differential operator $\Delta_{p}u := \Div(\abs{\nabla u}^{p-2}\nabla u)$. Namely, if $\rho$ is a…