Nonperturbative localization on the strip and Avila’s almost reducibility conjecture
Abstract
Abstract We prove nonperturbative Anderson localization and almost localization for a family of quasi-periodic operators on the strip. As an application, we establish Avila’s almost reducibility conjecture for Schrödinger operators with trigonometric potentials and all Diophantine frequencies. As part of our analysis, we derive a nonselfadjoint version of Haro and Puig’s formula connecting the Lyapunov exponents of the dual model to those of the original operator.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Forum of Mathematics Pi
- Publisher
- Cambridge University Press (CUP)
- Volume
- 14
- Publication date
- 1 January 2026
- Language
- EN