Related papers: Magnetic Neumann Laplacian on a sharp cone

We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle $\alpha$. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in…

A Laplacian eigenfunction on a two-dimensional manifold dictates some natural partitions of the manifold; the most apparent one being the well studied nodal domain partition. An alternative partition is revealed by considering a set of…

In this paper, we examine eigenfunctions of a generalized Landau Magnetic Laplacian that models the physics of an electron confined to a plane in a magnetic field orthogonal to the plane. This operator has an infinite dimensional null space…

We report on neutron-scattering results on the impact of a magnetic field on stripe order in the cuprate La$_{1.875}$Ba$_{0.125}$CuO$_4$. It is found that a 7 T magnetic field applied along the {\it c} axis causes a small but finite…

Spectrum of the Laplacian on spherical domains is analyzed from the point of view of the heat equation on the cone. The series solution to the heat equation on the cone is known to lead to a study of the Laplacian eigenvalue problem on…

We present a numerical study of the spectrum of the Laplacian in an unbounded strip with PT-symmetric boundary conditions. We focus on non-Hermitian features of the model reflected in an unusual dependence of the eigenvalues below the…

We derive a necessary condition for compactness of the weighted $\overline\partial$-Neumann operator on the space $L^2(\mathbb C^n,e^{-\varphi})$, under the assumption that the corresponding weighted Bergman space of entire functions has…

Key diagnostics of non-thermal plasmas, such as the position of the synchrotron self-absorption turnover or the Faraday rotation optical depth, depend crucially on the unobserved low-energy electron spectrum. We investigate the effect of…

We study spectral properties of the Neumann-Poincar\'e operator on planar domains with corners with particular emphasis on existence of continuous spectrum and pure point spectrum. We show that the rate of resonance at continuous spectrum…

For a Hermitian holomorphic vector bundle over a Hermitian manifold, we consider the Dolbeault Laplacian with $\overline\partial$-Neumann boundary conditions, which is a self-adjoint operator on the space of square-integrable differential…

The nodal set of a Laplacian eigenfunction forms a partition of the underlying manifold or graph. Another natural partition is based on the gradient vector field of the eigenfunction (on a manifold) or on the extremal points of the…

Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic…

We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if $u$ is a weak solution of $(-\Delta)^s u=f$ in $\Omega$, $\mathcal N_s u=0$ in $\Omega^c$, then $u$ is $C^\alpha$…

We investigate spectral properties of the Laplacian in $L^2(Q)$, where $Q$ is a tubular region in $\mathbb{R}^3$ of a fixed cross section, and the boundary conditions combined a Dirichlet and a Neumann part. We analyze two complementary…

In this article we prove that the spectrum of the Laplacian on $k$-forms over a noncompact flat manifold is always a connected closed interval of the nonnegative real line. The proof is based on a detailed decomposition of the structure of…

We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away…

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a…

Let $X$ be a finite-area non-compact hyperbolic surface. We study the spectrum of the Laplacian on random covering surfaces of X and on random unitary bundles over X. We show that there is a constant $c > 0$ such that, with probability…

For a closed Riemannian orbifold $O$, we compare the spectra of the Laplacian, acting on functions or differential forms, to the Neumann spectra of the orbifold with boundary given by a domain $U$ in $O$ whose boundary is a smooth manifold.…

This paper concerns the $L^2$ essential spectrum of the Laplacian $\Delta$ and the drift Laplacian $\Delta_f$ on complete Riemannian manifolds endowed with a weighted measure $e^{-f}d\;vol_g$. We prove that the essential spectrum of the…