Dynamical bounds for quasiperiodic Schr\"odinger operators with rough potentials
Svetlana Jitomirskaya, Rajinder Mavi
TL;DR
This paper proves dynamical bounds indicating localization for quasiperiodic Schrödinger operators with rough potentials, based on positive Lyapunov exponents, extending understanding of spectral properties in such systems.
Contribution
It introduces new dynamical bounds for quasiperiodic operators with piecewise Holder potentials, linking positive Lyapunov exponents to localization behavior.
Findings
Establishes localization-type dynamical bounds
Connects positive Lyapunov exponents with spectral localization
Applies to operators with rough, piecewise Holder potentials
Abstract
We establish localization type dynamical bounds as a corollary of positive Lyapunov exponents for general operators with quasiperiodic potentials defined by piecewise Holder functions.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quasicrystal Structures and Properties