Anderson localization for one-frequency quasi-periodic block operators with long-range interactions

Jian, Wenwen; Shi, Yunfeng; Yuan, Xiaoping

doi:10.1063/1.5089801

Cited by 11 publications

(6 citation statements)

References 30 publications

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“…Diophantine frequency, i.e they have to remove a Hausdorff zero measure set of Diophantine frequencies. For the multi-frequency and multidimensional case, one can consult [23,24,26,52,59,63] and the references therein. However, in physics applications, there is more interest in the case where α is a priori fixed as a Diophantine frequency.…”

Section: Introductionmentioning

confidence: 99%

Exact mobility edges for 1D quasiperiodic models

Wang¹,

Xu²,

You³

et al. 2021

Preprint

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Mobility edges (ME), i.e. critical energies which separate absolutely continuous spectrum and purely point spectrum, is an important issue in quantum physics. So far there are two experimentally feasible 1D quasiperiodic models that have been discovered to have exact mobility edge. However, all the theoretical studies have remained at the numerical level. In this paper, we rigorously prove the existence and give the precise location of the MEs for these models.

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Section: Introductionmentioning

confidence: 99%

Exact mobility edges for 1D quasiperiodic models

Wang¹,

Xu²,

You³

et al. 2021

Preprint

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“…An improvement of some long-range estimates of [BJ02] was proved by Avila-Jitomirskaya [AJ10]. We also mention the work of Jian-Shi-Yuan [JSY19] for which a non-perturbative AL was established for some quasi-periodic block operator with exponentially decaying long-range perturbation.…”

Section: Introduction and Main Resultsmentioning

confidence: 84%

Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation

Shi¹

2019

Preprint

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In this paper we study the multi-frequency quasi-periodic operator with Gevrey type perturbation. We establish the large deviation theorem (LDT) for multi-dimensional quasi-periodic operator under sub-exponentially decaying long-range perturbation, and then prove its pure point spectrum property. Based on the LDT and Aubry duality, we show the absence of point spectrum for 1D (exponentially decaying) long-range quasi-periodic operator with multi-frequency and small Gevrey potential (without transversality restriction). We also prove the positivity of Lebesgue measure of spectrum.

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“…where {v s |1 ≤ s ≤ b} are real analytic, nonconstant on T. Recently, this method was used to prove Anderson localization for the long-range quasi-periodic block operators [13] (…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Anderson localization for the Maryland model with long range interactions

Shi,

Yuan

2019

Preprint

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Anderson localization for one-frequency quasi-periodic block operators with long-range interactions

Abstract: In this paper, we study the quasi-periodic operators Hǫ,ω(x):

Cited by 11 publications

References 30 publications

Exact mobility edges for 1D quasiperiodic models

Exact mobility edges for 1D quasiperiodic models

Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation

Anderson localization for the Maryland model with long range interactions

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