Localization for Almost-Periodic Operators with Power-law Long-range Hopping: A Nash-Moser Iteration Type Reducibility Approach

Abstract

In this paper we develop a Nash-Moser iteration type reducibility approach to prove the (inverse) localization for some $d$-dimensional discrete almost-periodic operators with power-law long-range hopping. We also provide a quantitative lower bound on the regularity of the hopping. As an application, some results of \cite{Sar82, Pos83, Cra83, BLS83} are generalized to the power-law hopping case.

arXiv commentto appear in CMP

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Cited by in corpus (2)

• Stability of the gapless pure point spectrum of self-adjoint operators
• Perturbative diagonalization and spectral gaps of quasiperiodic operators on ${\ell }^2({\mathbb{Z}}^d)$ with monotone potentials