Related papers: Magnetic Dirichlet Laplacian in curved waveguides
We investigate the asymptotic spectral distribution of the twisted Laplacian associated with a real harmonic 1-form on a compact hyperbolic surface. In particular, we establish a sublinear lower bound on the number of eigenvalues in a…
We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a…
We consider the discrete spectrum of the Dirichlet Laplacian on a manifold consisting of two adjacent parallel strips or planar layers coupled by a finite number N of windows in the common boundary. If the windows are small enough, there is…
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 magnetic Laplacian associated to discrete analogs of funnels. We perturb the metric in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from possible…
We prove a quantitative uncertainty principle at low energies for the Laplacian on fairly general weighted graphs with a uniform explicit control of the constants in terms of geometric quantities. A major step consists in establishing lower…
The magnetic Laplacian (also called the line bundle Laplacian) on a connected weighted graph is a self-adjoint operator wherein the real-valued adjacency weights are replaced by unit complex-valued weights $\{\omega_{xy}\}_{xy\in E}$,…
We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We…
We consider a Laplacian on periodic discrete graphs. Its spectrum consists of a finite number of bands. In a class of periodic 1-forms, i.e., functions defined on edges of the periodic graph, we introduce a subclass of minimal forms with a…
We develop sharp upper bounds for energy levels of the magnetic Laplacian on starlike plane domains, under either Dirichlet or Neumann boundary conditions and assuming a constant magnetic field in the transverse direction. Our main result…
We prove sharp criteria on the behavior of radial curvature for the existence of asymptotically flat or hyperbolic Riemannian manifolds with prescribed sets of eigenvalues embedded in the spectrum of the Laplacian. In particular, we…
We will study the spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with contains periodic arrangement of inclusions. On the boundary of the waveguide we…
We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…
We consider Laplacians on periodic equilateral metric graphs. The spectrum of the Laplacian consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite number of flat…
In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the…
We study the magnetic Rayleigh-Taylor instability in three dimensions, with focus on the nonlinear structure and evolution that results from different initial field configurations. We study strong fields in the sense that the critical…
We analyze the spectrum of the Laplace operator, subject to homogeneous complex magnetic fields in the plane. For real magnetic fields, it is well-known that the spectrum consists of isolated eigenvalues of infinite multiplicities (Landau…
We study the location of the spectrum of the Laplacian on compact metric graphs with complex Robin-type vertex conditions, also known as $\delta$ conditions, on some or all of the graph vertices. We classify the eigenvalue asymptotics as…
In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint…