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arXiv · 2608.19130

Connectivity--Interference Competition in Coherent Transport on Percolated Hierarchical Small-World Networks

Miquéias Jacinto Cirino·Marcos César de Oliveira
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Abstract

Adding links generally improves classical transport by increasing the number of available paths. We show that coherent quantum transport can display the opposite behavior. Using continuous-time quantum walks on a percolated hierarchical small-world network, we identify a coherent overconnectivity penalty: root-to-boundary transport is maximized at intermediate bond probability and decreases as the network approaches full connectivity. The effect is quantified by the final-layer limiting probability $\chi_N$ and by the penalty $P_Q=1-\chi_N(p=1)/\max_p\chi_N(p)$, which measures the loss caused by making the architecture fully connected. The optimum results from a competition between shortcut-assisted spreading and interference-induced intra-layer recirculation. Spectral analysis shows that bond dilution creates motif-induced degeneracies and reorganizes the eigenstates connecting the root to the outermost layer. A comparison with dephased and classical transport shows that the non-monotonic landscape is not a purely geometrical percolation effect, but a coherent architecture-dependent phenomenon. These results provide a design principle for coherent transport in disordered photonic and quantum-network architectures.

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Miquéias Jacinto Cirino, Marcos César de Oliveira. 2026-08-19. Connectivity--Interference Competition in Coherent Transport on Percolated Hierarchical Small-World Networks. https://arxiv.org/abs/2608.19130

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