Abstract：We investigate 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 σ has interesting behaviors for different period q and parameter θ. We study the behavior of standard deviation with variation in walk steps, period, and θ. The standard deviation increases approximately linearly with θ and decreases with 1/q for θ∈(0,π/4), and increases approximately linearly with 1/q for θ∈[π/4,π/2). For θ∈(π/4, 3π/4), the transmission is larger than the reflection, with sensibility the diffussion will be accelerated. However, when q=2, the standard deviations are nearly the same, and when q>2, the standard deviation will decrease.
. [J]. Chin. Phys. Lett., 2013, 30(2): 20304-020304.
LI Min, ZHANG Yong-Sheng, GUO Gunag-Can. Quantum Random Walk in Periodic Potential on a Line. Chin. Phys. Lett., 2013, 30(2): 20304-020304.
2013, Vol. 30 
