Persistent homology and topological statistics of hyperuniform point clouds
Physical Review Research(2024)
摘要
Hyperuniformity, the suppression of density fluctuations at large length
scales, is observed across a wide variety of domains, from cosmology to
condensed matter and biological systems. Although the standard definition of
hyperuniformity only utilizes information at the largest scales, hyperuniform
configurations have distinctive local characteristics. However, the influence
of global hyperuniformity on local structure has remained largely unexplored;
establishing this connection can help uncover long-range interaction mechanisms
and detect hyperuniform traits in finite-size systems. Here, we study the
topological properties of hyperuniform point clouds by characterizing their
persistent homology and the statistics of local graph neighborhoods. We find
that varying the structure factor results in configurations with systematically
different topological properties. Moreover, these topological properties are
conserved for subsets of hyperuniform point clouds, establishing a connection
between finite-sized systems and idealized reference arrangements. Comparing
distributions of local topological neighborhoods reveals that the hyperuniform
arrangements lie along a primarily one-dimensional manifold reflecting an
order-to-disorder transition via hyperuniform configurations. The results
presented here complement existing characterizations of hyperuniform phases of
matter, and they show how local topological features can be used to detect
hyperuniformity in size-limited simulations and experiments.
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