Related papers: Absolutely continuous spectrum of perturbed Stark …

We consider Sch\"odinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if $\Delta +…

The one-dimensional Dirac operator with periodic potential $V=\begin{pmatrix} 0 & \mathcal{P}(x) \\ \mathcal{Q}(x) & 0 \end{pmatrix}$, where $\mathcal{P},\mathcal{Q}\in L^2([0,\pi])$ subject to periodic, antiperiodic or a general strictly…

In this paper we consider two classes of random Hamiltonians on $L^2(\RR^d)$ one that imitates the lattice case and the other a Schr\"odinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the…

The subject of this work are random Schroedinger operators on regular rooted tree graphs $\T$ with stochastically homogeneous disorder. The operators are of the form $H_\lambda(\omega) = T + U + \lambda V(\omega)$ acting in $\ell^2(\T)$,…

This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…

The aim of this paper is to construct an explicit potential for the Dirac operator that has purely singular continuous spectrum. The characteristic trait of this potential is that it consists of bumps whose distance is growing rapidly. This…

We continue the investigation of the existence of absolutely continuous (a.c.) spectrum for the discrete Schr\"odinger operator $\Delta+V$ on $\ell^2(\Z^d)$, in dimensions $d\geq 2$, for potentials $V$ satisfying the long range condition…

We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite…

We show that it is impossible to quantify the decay rate of a semi-uniformly stable operator semigroup based on sole knowledge of the spectrum of its infinitesimal generator. More precisely, given an arbitrary positive function $r$…

We prove stochastic stability of absolutely continuous invariant measures (ACIMs) for piecewise expanding $C^{1+\varepsilon}$ maps of the interval. For maps $\tau$ in the class $\mathcal{T}([0,1]; s, \varepsilon)$, we consider perturbed…

We consider small perturbations of expanding maps induced by skew-product mappings whose base dynamics are not invertible necessarily. Adopting a previously developed perturbative spectral approach, we show stability of the densities of the…

We study the spectra for a class of differential operators with asymptotically constant coefficients.These operators widely arise as the linearizations of nonlinear partial differential equations about patterns or nonlinear waves. We…

A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple,…

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…

We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum of the linearised operator in full generality and identify…

Almost commutative models provide a framework for Connes' work on the standard model of particle physics. These models are constructed as products of a the canonical spectral triple of a compact connected spin manifold with a finite…

We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…

The spectral propinquity is a distance, up to unitary equivalence, on the class of metric spectral triples. We prove in this paper that if a sequence of metric spectral triples converges for the propinquity, then the spectra of the Dirac…

We prove the almost sure existence of absolutely continuous spectrum at low disorder for the Anderson model on the simplest example of a product of a regular tree with a finite graph. This graph contains loops of unbounded size.

We consider random Schr\"odinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These…