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

Hiroaki S. Yamada

Chaos, Solitons & Fractals, 2018, vol. 109, issue C, 99-106

Abstract: 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.

Keywords: Localization; Delocalization; Long-range; Correlation; Bernoulli map (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:109:y:2018:i:c:p:99-106

DOI: 10.1016/j.chaos.2018.02.025

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