Related papers: On the singularities of the spectral shift functio…

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…

We consider a scalar Euclidean QFT with interaction given by a bounded, measurable function $V$ such that $V^{\pm}:=\lim_{w\to \pm\infty}V(w)$ exist. We find a field renormalization such that all the $n$-point connected Schwinger functions…

Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the spectrum of $A$ consists of two disjoint components $\sigma_0$ and $\sigma_1$. Let $V$ be a bounded operator on $\fH$, off-diagonal and $J$-self-adjoint with…

This article consists of two connected parts. In the first part, we study the shift invariant subspaces in certain $\mathcal{P}^2(\mu)$-spaces, which are the closures of analytic polynomials in the Lebesgue spaces $\mathcal{L}^2(\mu)$…

In exactly solvable quantum-mechanical systems, ladder and intertwining operators play a central role because, if they are found, the energy spectra can be obtained algebraically. In this paper, we propose the spectral intertwining relation…

We study spectral properties of Hamiltonians $\rH_{X,\gB,q}$ with $\delta'$-point interactions on a discrete set $X={x_k}_{k=1}^\infty\subset\R_+$. %at the centers $x_n$ on the positive half line in terms of energy forms. Using the form…

We obtain order sharp spectral estimates for the difference of resolvents of singularly perturbed elliptic operators $\mathbf{A}+\mathbf{V}_1$ and $\mathbf{A}+\mathbf{V}_2$ in a domain $\Omega\subseteq \mathbb{R}^\mathbf{N}$ with…

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an…

We consider the unperturbed operator $H_0 : = (-i \nabla - A)^2 + W$, self-adjoint in $L^2(\R^2)$. Here $A$ is a magnetic potential which generates a constant magnetic field $b>0$, and the edge potential $W$ is a non-decreasing non constant…

We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…

We consider interacting many particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent, z, such as random quantum systems and exclusion processes. In several d=1 and d=2…

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

We consider a compact perturbation $H_0 = S + K_0^* K_0$ of a self-adjoint operator $S$ with an eigenvalue $\lambda^\circ$ below its essential spectrum and the corresponding eigenfunction $f$. The perturbation is assumed to be "along" the…

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…

We study the spectrum of a one-dimensional Schroedinger operator perturbed by a fast oscillating potential. The oscillation period is a small parameter. The essential spectrum is found in an explicit form. The existence and multiplicity of…

We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field v. We prove that the associated discrete Schroedinger operator H can have one or two eigenvalues, situated as below…

This thesis report deals with the 1D Hubbard model and the quantum objects that diagonalize the normal ordered Hubbard hamiltonian, among those the so called PseudoFermions (PFs). These PFs have no residual energy interactions, are eta-spin…

We study the essential spectrum and Fredholm properties of integral and pseudodiferential operators associated to (maybe non-commutative) locally compact groups G. The techniques involve crossed product C*-algebras. We extend previous…

We study the manner in which a sequence of spectral shift functions $\xi(\cdot;H_j,H_{0,j})$ associated with abstract pairs of self-adjoint operators $(H_j, H_{0,j})$ in Hilbert spaces $\cH_j$, $j\in\bbN$, converge to a limiting spectral…

We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of…