[Xu, Xin-Ping] HuaZhong Normal Univ, Inst Particle Phys, Wuhan 430079, Peoples R China
; [Xu, Xin-Ping] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
In this paper, we consider continuous-time quantum walks (CTQWs) on a one-dimensional 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 space-time 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 walks (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 CTQWs and CTRWs. For fixed parameter m, the transport of CTRWs gets slower 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 patterns. 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.