Almost zero transfer in continuous-time quantum walks on weighted tree graphs

• URL: http://arxiv.org/abs/2404.04094v1
• Date: Fri, 5 Apr 2024 13:41:11 GMT
• Title: Almost zero transfer in continuous-time quantum walks on weighted tree graphs
• Authors: Rafael Vieira, Edgard P. M. Amorim,
• Abstract summary: We study continuous-time quantum walks on weighted tree graphs. We map Cayley trees $C_3,2$ and $C_3,3$ into these spider graphs and observe the same dependency.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the probability flux on the central vertex in continuous-time quantum walks on weighted tree graphs. In a weighted graph, each edge has a weight we call hopping. This hopping sets the jump rate of the particle between the vertices connected by the edge. Here, the edges of the central vertex (root) have a hopping parameter $J$ larger than those of the other edges. For star graphs, this hopping gives only how often the walker visits the central vertex over time. However, for weighted spider graphs $S_{n,2}$ and $S_{n,3}$, the probability on the central vertex drops with $J^2$ for walks starting from a state of any superposition of leaf vertices. We map Cayley trees $C_{3,2}$ and $C_{3,3}$ into these spider graphs and observe the same dependency. Our results suggest this is a general feature of such walks on weighted trees and a way of probing decoherence effects in an open quantum system context.

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