Svetlana Ya Jitomirskaya

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Although concrete operators with singular continuous spectrum have proliferated re-, we still don't really understand much about singular continuous spectrum. In part, this is because it is normally defined by what it isn't — neither pure point nor absolutely continuous. An important point of view, going back in part to Rodgers and Taylor [27,28], and(More)
We prove that one-dimensional Schrr odinger operators with even almost periodic potential have no point spectrum for a dense G in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense G in even if the frequency is an irrational with good Diophantine properties. x1. Introduction This(More)
We study the almost Mathieu operator (h λ,α,θ u)(n) = u(n + 1) + u(n − 1) + λ cos(παn + θ)u(n) on 2 (Z), and prove that the dual of point spectrum is absolutely continuous spectrum. We use this to show that for λ = 2 it has purely singular continuous spectrum for a.e. pairs (α, θ). The α's for which we prove this are explicit. Our main goal in this paper is(More)
ii c 2005 Mihai Stoiciu All Rights Reserved iii Acknowledgements I would like to express my deepest gratitude to my advisor, Professor Barry Simon, for his help and guidance during my graduate studies at Caltech. During the time I worked under his supervision, Professor Simon provided a highly motivating and challenging scientific environment, which was(More)
We examine various issues relevant to localization in the Anderson model. We show there is more to localization than exponentially localized states by presenting an example with such states but where x(t) 2 /t 2−δ is unbounded for any δ > 0. We show that the recently discovered instability of localization under rank one perturbations is only a weak(More)