Related papers: A magnetic eigenvalue bound in the disk

We prove an analogue of P\'olya's conjecture for the eigenvalues of the magnetic Schr\"odinger operator with Aharonov--Bohm potential on the disk, for Dirichlet and magnetic Neumann boundary conditions. This answers a question posed by R.…

We consider the Gel'fand-Calder\'on problem for a Schr\"odinger operator of the form $-(\nabla + iA)^2 + q$, defined on a ball $B$ in $\mathbb R^3$. We assume that the magnetic potential $A$ is small in $W^{s,3}$ for some $s>0$, and that…

We provide a purely variational proof of the existence of eigenvalues below the bottom of the essential spectrum for the Schr\"odinger operator with an attractive $\delta$-potential supported by a star graph, i.e. by a finite union of rays…

We prove a lower bound on the eigenvalues $\lambda_k$, $k\in\mathbb{N}$, of the Dirichlet Laplacian of a bounded domain $\Omega\subset\mathbb{R}^n$ of volume $V$: $$ \lambda_k \geq C_n\bigg( \delta\frac{k}{V}\bigg)^{2/n} $$ where $\delta$…

Eigenvalue behaviors of Schr\"odinger operator defined on $n$-dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\geq 2$, and lower…

We study the Schroedinger operator with a constant magnetic field in the exterior of a two-dimensional compact domain. Functions in the domain of the operator are subject to a boundary condition of the third type (Robin condition). In…

In this paper we consider the first eigenvalue $\lambda_1(\Omega)$ of the Grushin operator $\Delta_G:=\Delta_{x_1}+|x_1|^{2s}\Delta_{x_2}$ with Dirichlet boundary conditions on a bounded domain $\Omega$ of $\mathbb{R}^d=…

We study a model Schr\"odinger operator with constant magnetic field on an infinite wedge with Neumann boundary condition. The magnetic field is assumed to be tangent to a face. We compare the bottom of the spectrum to the model spectral…

Let $\Omega$ be a bounded domain in $\mathbb R^2$ with smooth boundary $\partial\Omega$, and let $\omega_h$ be the set of points in $\Omega$ whose distance from the boundary is smaller than $h$. We prove that the eigenvalues of the…

We present numerical minimizers for the first seven eigenvalues of the magnetic Dirichlet Laplacian with constant magnetic field in a wide range of field strengths. Adapting an approach by Antunes and Freitas, we use gradient descent for…

We consider the eigenvalue problem for the Schr\"odinger operator on bounded, convex domains with mixed boundary conditions, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its…

In this work, we use regularized determinant approach to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schr\"odinger operator $(-i\nabla - \textbf{\textup{A}})^{2} - b$ in…

In this paper, we analyze the magnetic Dirichlet-to-Neumann operator (D-to-N map) $\check \Lambda(b,\nu)$ on the exterior of the disk with respect to a magnetic potential $A_{b, \nu}=A^b + A_\nu$ where, for $b\in \mathbb R$ and $\nu \in…

We study two-dimensional magnetic Schr\"odinger operators with a magnetic field that is equal to b>0 for x > 0 and (-b) for x < 0. This magnetic Schr\"odinger operator exhibits a magnetic barrier at x=0. The unperturbed system is invariant…

The eigenvalue problem for the p-Laplace operator with p>1 on planar domains with the zero Dirichlet boundary condition is considered. The Constrained Descent Method and the Constrained Mountain Pass Algorithm are used in the Sobolev space…

We investigate spectral properties of the operator describing a quantum particle confined to a planar domain $\Omega$ rotating around a fixed point with an angular velocity $\omega$ and demonstrate several properties of its principal…

For Schr\"odinger operators on an interval with either convex or symmetric single-well potentials, and Robin or Neumann boundary conditions, the gap between the two lowest eigenvalues is minimised when the potential is constant. We also…

We obtain upper bounds for the first eigenvalue of the magnetic Laplacian associated to a closed potential $1$-form (hence, with zero magnetic field) acting on complex functions of a planar domain $\Omega$, with magnetic Neumann boundary…

We derive a sufficient condition for a Hermitian $N \times N$ matrix $A$ to have at least $m$ eigenvalues (counting multiplicities) in the interval $(-\epsilon, \epsilon)$. This condition is expressed in terms of the existence of a…

We compute the sum and number of eigenvalues for a certain class of magnetic Schrodinger operators in a domain with boundary. Functions in the domain of the operator satisfy a (magnetic) Robin condition. The calculations are valid in the…