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Quasiperiodic dynamics of a quantum walk on the line
Antoni Wójcik1, Tomasz Łuczak, Paweł Kurzyński
1Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland.
Abstract:
We study the dynamics of a generalization of a quantum coin walk on the line, which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations for recurrence phenomena observed by Bouwmeester et al. [Phys. Rev. A 61, 13410 (1999)]] in their optical Galton board experiment, and a description of a stroboscopic quantum walk given by Buerschaper and Burnett [quant-ph/0406039] through numerical simulations. We also provide heuristic explanations for the behavior of our model which show, in particular, that its dynamics can be viewed as a discrete version of Bloch oscillations.
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