Related papers: A magnetic eigenvalue bound in the disk

Given a closed Riemannian manifold $M$ and $b\geq2$ closed connected submanifolds $N_j\subset M$ of codimension at least $2$, we prove that the first non-zero eigenvalue of the domain $\Omega_\varepsilon\subset M$ obtained by removing the…

We study an inverse boundary value problem with partial data in an infinite slab in $\mathbb{R}^{n}$, $n\geq 3$, for the magnetic Schr\"{o}dinger operator with an $L^{\infty}$ magnetic potential and an $L^{\infty}$ electric potential. We…

We consider Schr\"odinger operators in $\mathbb R^d$ with complex potentials supported on a hyperplane and show that all eigenvalues lie in a disk in the complex plane with radius bounded in terms of the $L^p$ norm of the potential with…

Upper bounds of the first non-trivial eigenvalue $\lambda_1$ of the Laplace operator of a compact submanifold $M^n$ of Euclidean space $\R^{m+1}$, by means of a new technique, are obtained. Each of the upper bounds of $\lambda_1$ depends on…

The Landauer principle states that at least $k_B T \ln 2$ of energy is required to erase a 1-bit memory, with $k_B T$ the thermal energy of the system. We study the effects of inertia on this bound using as one-bit memory an underdamped…

We provide a characterization of the spectral minimum for a random Schr\"odinger operator of the form $H=-\Delta + \sum_{i \in \Z^d}q(x-i-\omega_i)$ in $L^2(\R^d)$, where the single site potential $q$ is reflection symmetric, compactly…

A two-dimensional Schr\"odinger operator with a constant magnetic field perturbed by a smooth compactly supported potential is considered. The spectrum of this operator consists of eigenvalues which accumulate to the Landau levels. We call…

Let $\Lambda\subset \mathbb{R}^d$ be a domain consisting of several cylinders attached to a bounded center. One says that $\Lambda$ admits a threshold resonance if there exists a non-trivial bounded function $u$ solving $-\Delta u=\nu u$ in…

Let $\Omega\subset \mathbb R^2$ be a bounded planar domain, with piecewise smooth boundary $\partial \Omega$. For $\sigma>0$, we consider the Robin boundary value problem \[ -\Delta f =\lambda f, \qquad \frac{\partial f}{\partial n} +…

We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is…

We consider the Schr\"odinger operator with a periodic potential on a quasi 1D continuous periodic model of armchair nanotubes in $\R^3$ in a uniform magnetic field (with amplitude $B\in \R$), which is parallel to the axis of the nanotube.…

We study the question of magnetic confinement of quantum particles on the unit disk $\ID$ in $\IR^2$, i.e. we wish to achieve confinement solely by means of the growth of the magnetic field $B(\vec x)$ near the boundary of the disk. In the…

Let $\mathcal{M}(\mathbb{R}^n)$ be the class of bounded away from one and infinity functions $p:\mathbb{R}^n\to[1,\infty]$ such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space…

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 consider the magnetic Robin Laplacian with a negative boundary parameter. Among a certain class of domains, we prove that the disk maximizes the ground state energy under the fixed perimeter constraint provided that the magnetic field is…

Let $f$ be an entire transcendental function of finite order and $\Delta$ be a forward invariant bounded Siegel disk for $f$ with rotation number in Herman's class $\mathcal{H}$. We show that if $f$ has two singular values with bounded…

We consider the multidimensional Borg-Levinson theorem of determining both the magnetic field $dA$ and the electric potential $V$, appearing in the Dirichlet realization of the magnetic Schr\"odinger operator $H=(-{\rm i}\nabla+A)^2+V$ on a…

In this paper we characterize the limiting behavior of the principal eigenvalue, $\s_1[-\D,\b,\O]$, of the boundary value problem \eqref{1.1} as the Lebesgue measure of the underlying domain, $\O$, tends to zero. Naturally, the domains $\O$…

For bound states of atoms and molecules of $N$ electrons we consider the corresponding $K$-particle reduced density matrices, $\Gamma^{(K)}$, for $1 \le K \le N-1$. Previously, eigenvalue bounds were obtained in the case of $K=1$ and…

We consider the ground state of the quantum Ising model with transverse field $h$ in one dimension in a finite volume \[ \Lambda{_{m}:=\{-m,-m+1,\ldots,m+L\}\ .}% \] For $h$ sufficiently large we prove a bound for the entanglement of the…