Ultraslow diffusion emerging from local symmetry breaking in quenched disorder

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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.
Funding Information
  • National Natural Science Foundation of China (62471496)
  • National Natural Science Foundation of China (62071496)
  • National Natural Science Foundation of China (62671629)
  • Central South University (2025ZZTS0610)

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