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

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.