Spectral analysis of hierarchical continuous-time quantum walks
Abstract
In this paper, we introduce hierarchical random walks at first. In this model, we use two types of random walkers, global and local walkers. The global walker chooses a local walker at every step, then the chosen local walker moves a single step. After that we construct the corresponding continuous-time quantum walks and discuss its spectral structures. Then we define multi-dimensional continuous-time quantum walk by taking a marginal distribution respect to the global walker.
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