We consider the spectral and dynamical properties of one-dimensional quantum
walks placed into homogenous electric fields according to a discrete version of
the minimal coupling principle. We show that for all irrational fields the
absolutely continuous spectrum of these systems is empty, and prove Anderson
localization for almost all (irrational) fields. This result closes a gap which
was left open in the original study of electric quantum walks: a spectral and
dynamical characterization of these systems for typical fields. Additionally,
we derive an analytic and explicit expression for the Lyapunov exponent of this
model. Making use of a connection between quantum walks and CMV matrices our
result implies Anderson localization for CMV matrices with a particular choice
of skew-shift Verblunsky coefficients as well as for quasi-periodic unitary
band matrices.Comment: 18 pages, 2 figure