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Anomalous Mobility Enhancement in Restricted Geometries

  • Yuval Zippin
  • Stanislav Burov
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Abstract

We investigate the effect of geometrical confinement on driven transport in anomalous media within the framework of the quenched trap model. The particle performs a biased random walk on a lattice, where quenched disorder introduces power-law distributed trapping times. We consider channels that are infinite along one direction and have a finite cross-section in the remaining d−1 directions. In the glassy regime, where α=T/Tg<1, we derive an analytical expression for the mean longitudinal displacement in the long-time and weak-force limits. We find the scaling ⟨ x∥(t)⟩ ∝ F∥αtαΩ−(1−α), where F∥>0 is the effective longitudinal force and Ω is the number of sites in a transverse cross-section. Thus, the anomalous mobility is enhanced for narrower channels. Our analytical result applies to general Bravais lattices in d dimensions with periodic transverse boundary conditions. Numerical simulations confirm the analytical predictions for different lattice geometries and show quantitative agreement even for channels with reflecting boundary conditions.

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Cite

BibTeXRIS
BibTeX
@misc{zippin2026anomalous,
  title = {{Anomalous Mobility Enhancement in Restricted Geometries}},
  author = {Yuval Zippin and Stanislav Burov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35324},
  eprint = {2610.35324},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35324},
}
RIS
TY  - UNPB
TI  - Anomalous Mobility Enhancement in Restricted Geometries
AU  - Yuval Zippin
AU  - Stanislav Burov
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35324
UR  - https://arxiv.org/abs/2610.35324
AB  - We investigate the effect of geometrical confinement on driven transport in anomalous media within the framework of the quenched trap model. The particle performs a biased random walk on a lattice, where quenched disorder introduces power-law distributed trapping times. We consider channels that are infinite along one direction and have a finite cross-section in the remaining d−1 directions. In the glassy regime, where α=T/T_g<1, we derive an analytical expression for the mean longitudinal displacement in the long-time and weak-force limits. We find the scaling ⟨ x_∥(t)⟩ ∝ F_∥^αt^αΩ^−(1−α), where F_∥>0 is the effective longitudinal force and Ω is the number of sites in a transverse cross-section. Thus, the anomalous mobility is enhanced for narrower channels. Our analytical result applies to general Bravais lattices in d dimensions with periodic transverse boundary conditions. Numerical simulations confirm the analytical predictions for different lattice geometries and show quantitative agreement even for channels with reflecting boundary conditions.
ER  -