In this paper, we study the stability of the absolutely continuous spectrum of onedimensional Stark operators under various classes of perturbations. Stark Schrödinger operators describe behavior of the charged particle in the constant electric field. The absolutely continuous spectrum is a manifestation of the fact that the particle described by the operator propagates to infinity at a rather ...

We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these. §0 Introduction Let (X,B, m, T ) be an invertible, ergodic measure preserving transformation of a σ-finite measure space, then there are no other σ-finite, m-abs...

In many natural situations, one observes a local system with many competing species that is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When the competition matrix is random, the number of SUs depends on the average value and variance of its entries. Here we consider the problem in the limit of wea...

Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and character...

Abstract. We prove several new results on the absolutely continuous spectrum of perturbed one-dimensional Stark operators. First, we find new classes of potentials, characterized mainly by smoothness condition, which preserve purely absolutely continuous spectrum. Then we establish stability of the absolutely continuous spectrum in more general situations, where imbedded singular spectrum may o...

Some new conditions are obtained for the absolutely continuous spectrum of a Stark operator to fill the entire real line. §