Related papers: On eigenvalue accumulation for non-self-adjoint ma…

The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-No\"el, Fournais, Kachmar and Raymond to prove the existence of bound states of a new…

We investigate the spectral properties of self-adjoint Schr\"odinger operators with attractive $\delta$-interactions of constant strength $\alpha > 0$ supported on conical surfaces in ${\mathbb R}^3$. It is shown that the essential spectrum…

We prove optimal spectral inequalities for Landau operators in full space and in arbitrary dimension. Spectral inequalities are lower bounds on the L 2 -mass of functions in spectral subspaces of finite energy when integrated over a…

We study the spectrum of a system of second order differential operator perturbed by a non-selfadjoint matrix valued potential. We prove that eigenvalues of the perturbed operator are located near the edges of the spectrum of the…

We develop the complex scaling method for the Dirichlet Laplacian in a domain with asymptotically cylindrical end. We define resonances as discrete eigenvalues of non-selfadjoint operators, obtained as deformations of the selfadjoint…

We consider Schr\"odinger operators with potentials satisfying a generalized bounded variation condition at infinity and an $L^p$ decay condition. This class of potentials includes slowly decaying Wigner--von Neumann type potentials…

The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as perturbations of selfadjoint linear operators. Two methods are…

In this work we prove that the eigenvalues of the $n$-dimensional massive Dirac operator $\mathscr{D}_0 + V$, $n\ge2$, perturbed by a possibly non-Hermitian potential $V$, are localized in the union of two disjoint disks of the complex…

Embedded point spectra of rank one singular perturbations of an arbitrary self-adjoint operator A on a Hilbert space H is studied. It is shown that these perturbations can be regarded as self-adjoint extensions of a densely defined closed…

Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $\Lambda_n\subset \mathbb{R}$, and we show that it converges to…

We consider the quantum mechanics of an electron trapped on an infinite band along the $x$-axis in the presence of the Morse-like perpendicular magnetic field $\vec{B}=-B_{0}e^{-\frac{2\pi}{a_{0}}x}\hat{k}$ with $B_{0}>0$ as a constant…

We prove a Rellich-Vekua type theorem for Schr\"{o}dinger operators with exponentially decreasing potentials on a class of lattices including square, triangular, hexagonal lattices and their ladders. We also discuss the unique continuation…

We obtain asymptotic resolvent expansions at the threshold of the essential spectrum for magnetic Schr\"odinger and Pauli operators in dimension three. These operators are treated as perturbations of the Laplace operator in…

This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two $2d$ Bloch eigenvalues which have a conical crossing. It turns out that in the…

Inequalities are derived for sums and quotients of eigenvalues of magnetic Schroedinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.

We consider a random Schro\"dinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the…

We consider a magnetic Laplacian $-\Delta_A=(id+A)^\star (id+A)$ on a noncompact hyperbolic surface $\mM $ with finite area. $A$ is a real one-form and the magnetic field $dA$ is constant in each cusp. When the harmonic component of $A$…

A model operator $H$ associated to a system of three-particles on the three dimensional lattice $\Z^3$ and interacting via pair non-local potentials is studied. The following results are proven: (i) the operator $H$ has infinitely many…

We consider the meromorphic operator-valued function 1-K(z) = 1-A(z)/z where A(z) is holomorphic on the domain D, and has values in the class of compact operators acting in a given Hilbert space. Under the assumption that A(0) is a…

For the magnetic Laplacian on a bounded planar domain, imposing Neumann boundary conditions produces eigenvalues below the lowest Landau level. If the domain has two boundary components and one imposes a Neumann condition on one component…