TY - JOUR

T1 - Propagation and spectral properties of quantum walks in electric fields

AU - Cedzich, Christopher

AU - Rybár, T.

AU - Werner, A. H.

AU - Alberti, A.

AU - Genske, M.

AU - Werner, R. F.

PY - 2013

Y1 - 2013

N2 - We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $, e.g., on whether $(2$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.

AB - We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $, e.g., on whether $(2$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.

U2 - 10.1103/PhysRevLett.111.160601

DO - 10.1103/PhysRevLett.111.160601

M3 - Article

VL - 111

SP - 160601

JO - Phys. Rev. Lett.

JF - Phys. Rev. Lett.

ER -