(De)localization in the prime Schrödinger operator

Oliveira, César R. de; Pellegrino, G. Q.

doi:10.1088/0305-4470/34/16/103

Cited by 8 publications

(12 citation statements)

References 14 publications

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“…Note that the non-stationarity can be satisfied for α ≥ 1. In addition, the LDT with mobility edges, has been found numerically for the onedimensional tight-binding model with the FFM model as the potential strength W decreases [16,17,18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 93%

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Delocalization in one-dimensional tight-binding models with fractal disorder

Yamada¹

2015

Eur. Phys. J. B

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In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states based on the normalized localization length by controlling the correlation and the disorder strength of the potential. In addition, the transition of the diffusive property of wavepacket dynamics is shown around the critical point.

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Section: Introductionmentioning

confidence: 93%

“…The N −dependence of Λ N with adequate numerical accuracy for the larger system size is necessary to perform the finitesize scaling analysis around the critical point. ∼ 2 17 . The averaging is taken over 2 12 realizations.…”

Section: Strong Disorder Regimementioning

confidence: 99%

Delocalization in one-dimensional tight-binding models with fractal disorder

Yamada¹

2015

Eur. Phys. J. B

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“…Bound (9) immediately follows. To prove part (b), one just takes A(N ) = A for every N. Since (B 1 (T )) (A (N (T )) = (A) > 0, the result follows from bound (9).…”

Section: A Quantum Dynamical Lower Bound Derived From Power-law Transmentioning

confidence: 99%

“…As in the case = ( √ 5−1)/2 and = 0, studied in [8], it is possible to improve this lower bound somewhat by exhibiting a suitable set A(N ) (stable under perturbation), studying its Lebesgue measure, and applying (9). The set A(N ) will again be given by the spectra of suitable periodic approximants, and the Lebesgue measure can again be bounded through a fine analysis of the trace map, akin to what is done in [8,19,27]; compare also [25].…”

Section: Sturmian Potentialsmentioning

confidence: 99%

Power-law bounds on transfer matrices and quantum dynamics in one dimension–II

Damanik

Sütõ

Tcheremchantsev

2004

Journal of Functional Analysis

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We establish quantum dynamical lower bounds for a number of discrete one-dimensional Schrödinger operators. These dynamical bounds are derived from power-law upper bounds on the norms of transfer matrices. We develop further the approach from part I and study many examples. Particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power-law bounds on transfer matrices. The models discussed in this paper include substitution models, Sturmian models, a hierarchical model, the prime model, and a class of moderately sparse potentials.

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“…E.g., among the latter examples the following one should be mentioned. There is a study of delocalization in binary "0" and "1" system and the sparse potential which takes different values for prime sites only [27]. It is in such a case that the very "sparse" model should also naturally be "nonstationary".…”

Section: Introductionmentioning

confidence: 99%

Localization in one-dimensional tight-binding model with chaotic binary sequences

Yamada¹

2018

Chaos, Solitons & Fractals

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We have numerically investigated localization properties in the one-dimensional tight-binding model with chaotic binary on-site energy sequences generated by a modified Bernoulli map with the stationary-nonstationary chaotic transition (SNCT). The energy sequences in question might be characterized by their correlation parameter B and the potential strength W. The quantum states resulting from such sequences have been characterized in the two ways: Lyapunov exponent at band centre and the dynamics of the initially localized wavepacket. Specifically, the B−dependence of the relevant Lyapunov exponent's decay is changing from linear to exponential one around the SNCT (B ≃ 2). Moreover, here we show that even in the nonstationary regime, mean square displacement (MSD) of the wavepacket is noticeably suppressed in the long-time limit (dynamical localization). The B−dependence of the dynamical localization lengths determined by the MSD exhibits a clear change in the functional behaviour around SNCT, and its rapid increase gets much more moderate one for B ≥ 2. Moreover we show that the localization dynamics for B > 3/2 deviates from the one-parameter scaling of the localization in the transient region.

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(De)localization in the prime Schrödinger operator

Cited by 8 publications

References 14 publications

Delocalization in one-dimensional tight-binding models with fractal disorder

Delocalization in one-dimensional tight-binding models with fractal disorder

Power-law bounds on transfer matrices and quantum dynamics in one dimension–II

Localization in one-dimensional tight-binding model with chaotic binary sequences

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