Exact Nonlinear Active Microrheology in Diffusive Single-File Systems
Abstract
Active microrheology probes a crowded medium by forcing a tracer and measuring its response. In single-file transport, where particles cannot overtake, a constant force F produces a subballistic displacement ⟨ Xt⟩≃ √t ξ(F) together with a persistent bath deformation. Despite decades of work, the exact nonlinear response at arbitrary force has remained confined to a few special solvable models. Here we remove this restriction by combining recent advances in hydrodynamic transport coefficients, a pressure-balance formulation of the local drive, and single-file duality, which eliminates the resulting moving boundary. This yields a closed exact boundary-value problem for general diffusive single files, determining both ξ(F) and the full density profile. For overdamped Brownian particles with general interactions, all microscopic interaction details enter only through the equilibrium equation of state, bringing realistic interacting systems, including finite-width quasi-one-dimensional channels, within exact reach. The solution also reveals universal global laws; in particular, the bath-density dipole is fixed by the applied force independently of the interaction potential.
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BibTeX
@misc{grabsch2026exact,
title = {{Exact Nonlinear Active Microrheology in Diffusive Single-File Systems}},
author = {Aurélien Grabsch and Olivier Bénichou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18733},
eprint = {2609.18733},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18733},
}
RIS
TY - UNPB
TI - Exact Nonlinear Active Microrheology in Diffusive Single-File Systems
AU - Aurélien Grabsch
AU - Olivier Bénichou
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18733
UR - https://arxiv.org/abs/2609.18733
AB - Active microrheology probes a crowded medium by forcing a tracer and measuring its response. In single-file transport, where particles cannot overtake, a constant force F produces a subballistic displacement ⟨ X_t⟩≃ √t ξ(F) together with a persistent bath deformation. Despite decades of work, the exact nonlinear response at arbitrary force has remained confined to a few special solvable models. Here we remove this restriction by combining recent advances in hydrodynamic transport coefficients, a pressure-balance formulation of the local drive, and single-file duality, which eliminates the resulting moving boundary. This yields a closed exact boundary-value problem for general diffusive single files, determining both ξ(F) and the full density profile. For overdamped Brownian particles with general interactions, all microscopic interaction details enter only through the equilibrium equation of state, bringing realistic interacting systems, including finite-width quasi-one-dimensional channels, within exact reach. The solution also reveals universal global laws; in particular, the bath-density dipole is fixed by the applied force independently of the interaction potential.
ER -