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arXiv · 1210.3112

Quantum random walk in periodic potential on a line

Min Li·Yong-Sheng Zhang·Guang-Can Guo
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Abstract

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 $σ$ has interesting behaviors for different period $q$ and parameter $θ$. We studied 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 $θ\in(0,π/4)$, and increases approximately linearly with $1/q$ for $θ\in[π/4,π/2)$. When $q=2$, the standard deviation is lazy for $θ\in[π/4+nπ,3π/4+nπ],n\in Z$.

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Min Li, Yong-Sheng Zhang, Guang-Can Guo. 2012-10-15. Quantum random walk in periodic potential on a line. https://doi.org/10.1088/0256-307x%2F30%2F2%2F020304

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