Quantum random walk in periodic potential on a line

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 $\sigma$ 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 $\theta \in [\pi /4+n\pi ,3\pi /4+n\pi ],n\in Z$.

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Cited by in corpus (1)

• Localization and Recurrence of Quantum Walk in Periodic Potential on a Line