2019/10/31 by Marcelo A. Pires, Sílvio M. Duarte Queirós · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.102.012104
published as Phys. Rev. E 102, 012104 (2020) · Updated version, close to the published one
arxiv created 2020/07/20 · arxiv updated 2020/07/30
We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse and Rudin-Shapiro. We use a generalized Hadamard coin \widehat CH as well as a generalized Fourier coin \widehat CK. We verify the QW experiences a slowdown of the wavepacket spreading --- σ2 (t) ∼ tα --- by the aperiodic jumps whose exponent, α, depends on the type of aperiodicity. Additional aperiodicity-induced effects also emerge, namely: (i) while the superdiffusive regime (1<α<2) is predominant, α displays an unusual sensibility with the type of coin operator where the more pronounced differences emerge for the Rudin-Shapiro and random protocol; (ii) even though the angle θ of the coin operator is homogeneous in space and time, there is a nonmonotonic dependence of α with θ. Fingerprints of the aperiodicity in the hoppings are also found when additional distributional measures such as Shannon entropy, IPR, Jensen-Shannon dissimilarity, and kurtosis are computed. Finally, we argue the spin-lattice entanglement is enhanced by aperiodic jumps.