1210.3112 (Min Li et al.)

Quantum random walk in periodic potential on a line    [PDF]

Min Li, Yong-Sheng Zhang, Guang-Can Guo

We investigated the discrete-time quantum random walks on a line in periodic potential. The probability distribution with periodic potential is more complex compared to the normal quantum walks, and the standard deviation $\sigma$ has interesting behaviors for different period $q$ and parameter $\theta$. We studied the behavior of standard deviation with variation in walk steps, period, and $\theta$. The standard deviation increases approximately linearly with $\theta$ and decreases with $1/q$ for $\theta\in(0,\pi/4)$, and increases approximately linearly with $1/q$ for $\theta\in[\pi/4,\pi/2)$. When $q=2$, the standard deviation is lazy for $\theta\in[\pi/4+n\pi,3\pi/4+n\pi],n\in Z$.

View original: http://arxiv.org/abs/1210.3112