arXiv subjects

Svetlana Ya. Jitomirskaya

Publications and source records attributed to Svetlana Ya. Jitomirskaya.

3 recordsLinked to original sources

arXiv2003

Nonperturbative localization

Study of fine spectral properties of quasiperiodic and similar discrete Schrödinger operators involves dealing with problems caused by small denominators, and until recently was only possible using perturbative methods, requiring certain small parameters and complicated KAM-type schemes. We review the recently developed nonperturbative methods for such study which lead to stronger results and are significantly simpler. Numerous applications mainly due to J. Bourgain, M. Goldstein, W. Schlag, and the author are also discussed.

math-ph↗

arXiv1999

Metal-insulator transition for the almost Mathieu operator

We prove that for Diophantine \om and almost every þ, the almost Mathieu operator, (H_{ω,λ,θ}Ψ)(n)=Ψ(n+1) + Ψ(n-1) + λ\cos 2π(ωn +θ)Ψ(n), exhibits localization for λ> 2 and purely absolutely continuous spectrum for λ< 2. This completes the proof of (a correct version of) the Aubry-André conjecture.

math.SP↗

arXiv1994

Singular continuous spectrum is generic

In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense $G_δ$.

math.SP↗