Quantum Random Walk in Periodic Potential on a Line
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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.
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Cite this article:
LI Min, ZHANG Yong-Sheng, GUO Gunag-Can. Quantum Random Walk in Periodic Potential on a Line[J]. Chin. Phys. Lett., 2013, 30(2): 020304. DOI: 10.1088/0256-307X/30/2/020304
LI Min, ZHANG Yong-Sheng, GUO Gunag-Can. Quantum Random Walk in Periodic Potential on a Line[J]. Chin. Phys. Lett., 2013, 30(2): 020304. DOI: 10.1088/0256-307X/30/2/020304
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LI Min, ZHANG Yong-Sheng, GUO Gunag-Can. Quantum Random Walk in Periodic Potential on a Line[J]. Chin. Phys. Lett., 2013, 30(2): 020304. DOI: 10.1088/0256-307X/30/2/020304
LI Min, ZHANG Yong-Sheng, GUO Gunag-Can. Quantum Random Walk in Periodic Potential on a Line[J]. Chin. Phys. Lett., 2013, 30(2): 020304. DOI: 10.1088/0256-307X/30/2/020304
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