Non-perturbative localization for quasi-periodic Jacobi block matrices

2023/09/07 by Han, Rui, Schlag, Wilhelm · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2309.03423

Abstract

We prove non-perturbative Anderson localization for quasi-periodic Jacobi block matrix operators assuming non-vanishing of all Lyapunov exponents. The base dynamics on tori \mathbbT^b is assumed to be a Diophantine rotation. Results on arithmetic localization are obtained for b=1, and applications to the skew shift, stacked graphene, XY spin chains, and coupled Harper models are discussed.

Cited by

• Hölder continuity of the integrated density of states for quasi-periodic Jacobi block matrices

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