Quantum Localization in Geometric Complex Networks
Abstract
Quantum localization, the phenomenon by which wave diffusion is halted, here understood as the superposition of propagating waves, can have many different origins, such as onsite random potentials in Anderson localization. However, some systems exhibit complex geometries and could potentially reproduce similar results without external potentials. In this work, we study how localization of single particle states is affected by the underlying topology of a simple but highly predictive complex network model: the geometric soft configuration model 𝕊1. By tuning the model's temperature and heterogeneity parameters, we are able to generate different structural patterns and focus on the transition from a small-world to a non-small-world regime. Our study suggests that small-world networks tend to have extended states, which spread the whole system's size, in contrast to non-small-world networks which tend to localize, showing how complex connectivity can play the role assigned to random energetic disorder.
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BibTeX
@misc{lewensteinsanpera2026quantum,
title = {{Quantum Localization in Geometric Complex Networks}},
author = {Jan Lewenstein-Sanpera and Tobias Grass and M. Àngeles Serrano and Bruno Juliá-Díaz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15874},
eprint = {2610.15874},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15874},
}
RIS
TY - UNPB
TI - Quantum Localization in Geometric Complex Networks
AU - Jan Lewenstein-Sanpera
AU - Tobias Grass
AU - M. Àngeles Serrano
AU - Bruno Juliá-Díaz
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15874
UR - https://arxiv.org/abs/2610.15874
AB - Quantum localization, the phenomenon by which wave diffusion is halted, here understood as the superposition of propagating waves, can have many different origins, such as onsite random potentials in Anderson localization. However, some systems exhibit complex geometries and could potentially reproduce similar results without external potentials. In this work, we study how localization of single particle states is affected by the underlying topology of a simple but highly predictive complex network model: the geometric soft configuration model 𝕊^1. By tuning the model's temperature and heterogeneity parameters, we are able to generate different structural patterns and focus on the transition from a small-world to a non-small-world regime. Our study suggests that small-world networks tend to have extended states, which spread the whole system's size, in contrast to non-small-world networks which tend to localize, showing how complex connectivity can play the role assigned to random energetic disorder.
ER -