  A quantum random walk model is established on a one-dimensional periodic
lattice that fluctuates between two possible states. This model is defined by
Lindblad rate equations that incorporate the transition rates between the two
lattice states. Leveraging the system's symmetries, the particle velocity can
be described using a finite set of equations, even though the state space is of
infinite dimension. These equations yield an analytical expression for the
velocity in the long-time limit, which is employed to analyze the
characteristics of directed motion. Notably, the velocity can exhibit multiple
inversions, and to achieve directed motion, distinct, nonzero transition rates
between lattice states are required.
