2013/07/31 by C. -I. Chou, C. -L. Ho · 1 citation
Mathematics · Physics and Astronomy · #cond-mat.other #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1674-1056/23/11/110302
published as Chin. Phys. B 23 (2014) 110302 · 12 pages, 14 figures. References updated, sign typos in Eqs. (2.2) and (2.5) corrected
arxiv created 2014/11/28 · arxiv updated 2015/06/16
We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness, we assume the walker's coin state is unaffected at sites without potential, and is rotated in an unbiased way according to Hadamard matrix at sites with potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks were studied numerically. It is found that of the six cases, four cases display significant localization effect, where the walker is confined in the neighborhood of the origin for sufficiently long times. Associated with such localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.