Related papers: A priori estimates for the Hill and Dirac operator…

We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…

We consider discrete one-dimensional random Schroedinger operators with decaying matrix-valued, independent potentials. We show that if the l^2-norm of this potential has finite expectation value with respect to the product measure then…

In this article we present comparisons between the spectrum of a one-dimensional Schr\"odinger operator for a particular periodic potential and for its restriction to a finite number of sites. We deduce from this finite, but large, number…

The complete expression of the heavy quark-antiquark potential up to order $1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use that expression and a mapping, assumed to be valid at large distances, between Wilson…

We present a Dirac quantization of generic single-horizon black holes in two-dimensional dilaton gravity. The classical theory is first partially reduced by a spatial gauge choice under which the spatial surfaces extend from a black or…

We numerically find out the spectrum of the $3$ spin $1$ Dirac operators found in~\cite{ApbPP}. We give an analytic and numerical proof that they are unitarily inequivalent. Since these operators come paired with an anticommuting chirality…

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on…

We present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this review forms an applicable framework for the complete solution…

Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived…

We discuss how to generalize a Dirac operator such that the solution of a Dirac equation is of bounded variation rather than continuous. We build the spectral theory for generalized Dirac operators and discuss the connection between them…

Let $l_{n}$ be the length of the $n$-th instability interval of the Hill operator $Ly=-y^{\prime\prime}+q(x)y$. We obtain that if $l_{n}=o(n^{-2})$ then $c_{n}=o(n^{-2})$, where $c_{n}$ are the Fourier coefficients of $q$. Using this…

The Hill operators $Ly=-y"+v(x)y$, considered with complex valued $\pi$-periodic potentials $v$ and subject to periodic, antiperiodic or Neumann boundary conditions have discrete spectra. For sufficiently large $n,$ close to $n^2$ there are…

This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…

We consider a first order operator with a smooth periodic 3x3 matrix potential on the real line. It is the Lax operator for the periodic vector NLS equation. Its spectrum covers the real line and it is union of the spectral bands of…

Let $\bigl\{X_k\bigr\}_{k \in \mathbb{Z}} \in \mathbb{L}^2(\mathcal{T})$ be a stationary process with associated lag operators ${\boldsymbol{\cal C}}_h$. Uniform asymptotic expansions of the corresponding empirical eigenvalues and…

In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by $\sigma \cdot F(-i\nabla)$, where…

In this paper we discuss a connection between Dirac operators on configuration spaces and Yang-Mills quantum field theory. We first show that the Hamilton operators of the self-dual and anti-self-dual sectors of a Yang-Mills quantum field…

We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…

We propose a method for finding gaps in the spectrum of a differential operator. When applied to the one-dimensional Hamiltonian of the quartic oscillator, a simple algebraic algorithm is proposed that, step by step, separates with a…

We consider the Schr\"odinger operator $H$ on the half-line with a periodic potential $p$ plus a compactly supported potential $q$. For generic $p$, its essential spectrum has an infinite sequence of open gaps. We determine the asymptotics…