85 citations · 177 across the 5 of their papers we have counts for
5 papers
Computer Validation of Open Gaps for the Almost Mathieu Operator with Critical Coupling
Jordi-Lluís Figueras, Joaquim Puig
We present some computer assisted methods to prove the existence of spectral gaps for the Almost Mathieu operator at critical coupling and give rigorous numerical estimates on thei…
Quasi-periodically driven quantum systems
Albert Verdeny, Joaquim Puig, Florian Mintert
Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well under…
Strange Nonchaotic Attractors in Harper Maps
Alex Haro, Joaquim Puig
We study the existence of Strange Nonchaotic Attractors (SNA) in the family of Harper maps, proving that they are typical but not robust in this family. Our approach is based on th…
A Nonperturbative Eliasson's Reducibility Theorem
Joaquim Puig
This paper is concerned with discrete, one-dimensional Schrödinger operators with real analytic potentials and one Diophantine frequency. Using localization and duality we show tha…
Cantor Spectrum for the Almost Mathieu Operator. Corollaries of localization,reducibility and duality
Joaquim Puig
In this paper we use results on reducibility, localization and duality for the Almost Mathieu operator, \[ (H_{b,ϕ} x)_n= x_{n+1} +x_{n-1} + b \cos(2 πn ω+ ϕ)x_n \] on $l^2(\mathbb…