title: Quasiperiodic dynamics of a quantum walk on the line.
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.
authors.affiliation: Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland.
authors.forename: Antoni
authors.initials: A
authors.lastname: Wójcik
authors.forename: Tomasz
authors.initials: T
authors.lastname: Łuczak
authors.forename: Paweł
authors.initials: P
authors.lastname: Kurzyński
authors.forename: Andrzej
authors.initials: A
authors.lastname: Grudka
authors.forename: Małgorzata
authors.initials: M
authors.lastname: Bednarska