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Peer-reviewedCC BY 4.0Physical Review Research

Ultraslow diffusion emerging from local symmetry breaking in quenched disorder

  • Jin Liu1
  • Rainer Klages2,3
  • Huihai Wang1
  • Kehui Sun1
  1. 1Central South University
  2. 2Queen Mary University of London
  3. 3London Mathematical Laboratory
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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.

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Cite

BibTeXRIS
BibTeX
@article{liu2026ultraslow,
  title = {{Ultraslow diffusion emerging from local symmetry breaking in quenched disorder}},
  author = {Jin Liu and Rainer Klages and Huihai Wang and Kehui Sun},
  journal = {Physical Review Research},
  year = {2026},
  month = oct,
  doi = {10.1103/cvmv-86bh},
  url = {https://link.aps.org/doi/10.1103/cvmv-86bh},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
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  - 2026/10/14
JO  - Physical Review Research
DO  - 10.1103/cvmv-86bh
UR  - https://link.aps.org/doi/10.1103/cvmv-86bh
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.
SN  - 2643-1564
ER  -