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Peer-reviewedCC BY 4.0Reports on Progress in Physics

Transverse geometry reshapes current and tracer fluctuation amplitudes in quasi-one-dimensional single files

  • Olivier Bénichou
  • Aurélien Grabsch
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Abstract

Single-file transport means no overtaking: particles move in a narrow channel while preserving their longitudinal order. This simple constraint has profound dynamical consequences, most notably tracer subdiffusion, and has made single-file transport a paradigmatic form of confined many-body motion, observed from molecular transport in zeolites to single-file diffusion of colloids in narrow channels. A common modelling approach assumes that, once overtaking is suppressed, finite-width effects can be discarded or represented by an effective particle size in a strictly one-dimensional model. Starting from the Brownian dynamics in the full confined geometry, we instead derive the exact large-scale one-dimensional fluctuating-hydrodynamic equation governing the coarse-grained line density. Its transport coefficients are fixed by the confined equilibrium equation of state, through which the transverse geometry remains encoded in the one-dimensional description. Consequently, transverse geometry leaves the t 1 / 2 single-file scaling unchanged but can qualitatively reshape the density dependence of the current and tracer fluctuation amplitudes. In the minimal hard-core setting, this yields a collective diffusivity that can become non-monotonic in density for sufficiently wide no-passing channels. This geometric non-monotonicity propagates to exact large-scale predictions for the amplitudes of integrated-current fluctuations and tracer-displacement fluctuations. The effect is robust to the interaction potential, channel geometry, initial preparation and microscopic dynamics. Quasi-one-dimensional single-file transport therefore defines a distinct regime in which forbidding overtaking does not erase geometry from collective transport.

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Cite

BibTeXRIS
BibTeX
@article{benichou2026transverse,
  title = {{Transverse geometry reshapes current and tracer fluctuation amplitudes in quasi-one-dimensional single files}},
  author = {Olivier Bénichou and Aurélien Grabsch},
  journal = {Reports on Progress in Physics},
  year = {2026},
  month = sep,
  doi = {10.1088/1361-6633/ae9afb},
  eprint = {2606.10991},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05752788v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Transverse geometry reshapes current and tracer fluctuation amplitudes in quasi-one-dimensional single files
AU  - Olivier Bénichou
AU  - Aurélien Grabsch
PY  - 2026
DA  - 2026/09/09
JO  - Reports on Progress in Physics
DO  - 10.1088/1361-6633/ae9afb
UR  - https://hal.science/hal-05752788v1
AB  - Single-file transport means no overtaking: particles move in a narrow channel while preserving their longitudinal order. This simple constraint has profound dynamical consequences, most notably tracer subdiffusion, and has made single-file transport a paradigmatic form of confined many-body motion, observed from molecular transport in zeolites to single-file diffusion of colloids in narrow channels. A common modelling approach assumes that, once overtaking is suppressed, finite-width effects can be discarded or represented by an effective particle size in a strictly one-dimensional model. Starting from the Brownian dynamics in the full confined geometry, we instead derive the exact large-scale one-dimensional fluctuating-hydrodynamic equation governing the coarse-grained line density. Its transport coefficients are fixed by the confined equilibrium equation of state, through which the transverse geometry remains encoded in the one-dimensional description. Consequently, transverse geometry leaves the t 1 / 2 single-file scaling unchanged but can qualitatively reshape the density dependence of the current and tracer fluctuation amplitudes. In the minimal hard-core setting, this yields a collective diffusivity that can become non-monotonic in density for sufficiently wide no-passing channels. This geometric non-monotonicity propagates to exact large-scale predictions for the amplitudes of integrated-current fluctuations and tracer-displacement fluctuations. The effect is robust to the interaction potential, channel geometry, initial preparation and microscopic dynamics. Quasi-one-dimensional single-file transport therefore defines a distinct regime in which forbidding overtaking does not erase geometry from collective transport.
SN  - 0034-4885
SN  - 1361-6633
ER  -