This analysis introduces hierarchical random walks and explores spectral features in quantum systems, suggesting new insights.
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 walks by taking a marginal distribution respect to the global walker.
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Akahori et al. (2026) studied this question.
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