## Continuous-time quantum walks on one-dimension regular networks

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Xu, Xinping

Liu, Feng

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In this paper, we consider continuous-time quantum walks (CTQWs) on
one-dimension ring lattice of N nodes in which every node is connected to its
2m nearest neighbors (m on either side). In the framework of the Bloch function
ansatz, we calculate the spacetime transition probabilities between two nodes
of the lattice. We find that the transport of CTQWs between two different nodes
is faster than that of the classical continuous-time random walk (CTRWs). The
transport speed, which is defined by the ratio of the shortest path length and
propagating time, increases with the connectivity parameter m for both the
CTQWs and CTRWs. For fixed parameter m, the transport of CTRWs gets slow with
the increase of the shortest distance while the transport (speed) of CTQWs
turns out to be a constant value. In the long time limit, depending on the
network size N and connectivity parameter m, the limiting probability
distributions of CTQWs show various paterns. When the network size N is an even
number, the probability of being at the original node differs from that of
being at the opposite node, which also depends on the precise value of
parameter m.

Comment: Typos corrected and Phys. ReV. E comments considered in this version

Comment: Typos corrected and Phys. ReV. E comments considered in this version

##### Keywords

Quantum Physics