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

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 similar or equal to 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 <greater than cir equal tq > 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. (C) 2018 Elsevier Ltd. All rights reserved.