Continuous-time quantum walks on one-dimensional regular networks.
Continuous-time quantum walks on one-dimensional regular networks.
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DOI：
10.1103/physreve.77.061127
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发表时间：
2008-01
期刊：
影响因子：
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通讯作者：
Xin-Ping Xu
中科院分区：
文献类型：
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作者：
Xin-Ping Xu
在本文中，我们考虑连续时间量子行走（CTQWs）在一个一维环格的N个节点，其中每个节点是连接到它的2m个最近的邻居（m在任何一侧）。在Bloch函数近似的框架下，我们计算了格点之间的时空跃迁几率。我们发现，CTQWs在两个不同的节点之间的传输速度比经典的连续时间随机游动（CTRWs）。传输速度，这是由最短路径长度和传播时间的比值定义的，增加与CTQWs和CTRW的连接性参数m。对于固定的参数m，随着最短距离的增加，CTRW的传输变慢，而CTQW的传输（速度）是一个常数。在长时间极限下，依赖于网络规模N和连通性参数m，CTQW的极限概率分布表现出不同的模式。当网络规模N为偶数时，处于原始节点的概率与处于相对节点的概率不同，这也取决于参数m的精确值。
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 .