Ultraslow diffusion emerging from local symmetry breaking in quenched disorder
Abstract
Many dynamical systems operate in disordered environments. In this Letter, we investigate how quenched randomness modifies particle diffusion. We show that, in finite-strength potential landscapes, low disorder densities can induce logarithmically ultraslow diffusion. The underlying mechanism originates from local symmetry breaking in particular potential configurations: Barrier-well structures form directional channels, causing particles to undergo hierarchical capture, escape, and recapture processes. A coarse-grained channel theory yields an approximate scaling prediction for the mean-square displacement. Counterintuitively, when the disorder density reaches the fully disordered limit, the system returns to normal diffusion, revealing a nontrivial, nonmonotonic relationship between disorder density and transport type. This mechanism is observed in both nonlinear maps and stochastic systems.
Versions
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BibTeX
@misc{liu2026ultraslow,
title = {{Ultraslow diffusion emerging from local symmetry breaking in quenched disorder}},
author = {Jin Liu and Rainer Klages and Huihai Wang and Kehui Sun},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00831},
eprint = {2611.00831},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00831},
}
RIS
TY - UNPB
TI - Ultraslow diffusion emerging from local symmetry breaking in quenched disorder
AU - Jin Liu
AU - Rainer Klages
AU - Huihai Wang
AU - Kehui Sun
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00831
UR - https://arxiv.org/abs/2611.00831
AB - Many dynamical systems operate in disordered environments. In this Letter, we investigate how quenched randomness modifies particle diffusion. We show that, in finite-strength potential landscapes, low disorder densities can induce logarithmically ultraslow diffusion. The underlying mechanism originates from local symmetry breaking in particular potential configurations: Barrier-well structures form directional channels, causing particles to undergo hierarchical capture, escape, and recapture processes. A coarse-grained channel theory yields an approximate scaling prediction for the mean-square displacement. Counterintuitively, when the disorder density reaches the fully disordered limit, the system returns to normal diffusion, revealing a nontrivial, nonmonotonic relationship between disorder density and transport type. This mechanism is observed in both nonlinear maps and stochastic systems.
ER -