Nonequilibrium phase transition in single-file transport at high crowding

TL;DR

The paper identifies a nonequilibrium phase transition in a homogeneous, closed one-dimensional BASEP system at high particle crowding, separating a jammed, thermally activated regime from a high-current regime mediated by solitary cluster waves. It introduces a unit-displacement law that yields $J=(\rho-\rho_c)\,v_{\rm sol}$ with $\rho_c=\frac{n_b}{\lceil n_b\sigma\rceil}$ and $v_{\rm sol}=\frac{\lceil n_b\sigma\rceil}{\tau_{\rm sol}}$, and shows phase diagrams in $(\sigma,\rho)$ and $(f,\rho)$ that reveal how the transition depends on cluster size $n_b$ and drag $f$. The transition also alters current-fluctuation universality from KPZ to EW, as $C(t)$ decays with exponents $-4/3$ or $-3/2$ depending on $J''(\rho)$, illustrating a deep link between soliton transport and fluctuation scaling. These findings, supported by Brownian cluster dynamics and extensive computation, suggest that high-crowding phase behavior is robust across periodic potentials and may inform experiments with colloids and biological transport in crowded, periodic landscapes.

Abstract

Driven particle transport in crowded and confining environments is fundamental to diverse phenomena across physics, chemistry, and biology. A main objective in studying such systems is to identify novel emergent states and phases of collective dynamics. Here, we report on a nonequilibrium phase transition occurring in periodic structures at high particle densities. This transition separates a weak-current phase of thermally activated transport from a high-current phase of solitary wave propagation. It is reflected also in a change of universality classes characterizing correlations of particle current fluctuations. Our findings demonstrate that sudden changes to high current states can occur when increasing particle densities beyond critical values.

Figures (4)

• Figure 1: Particle current $J(\rho)$ as a function of particle density $\rho$ for three particle diameters (a) $\sigma=4/5$ (b) $1/4$, and (c) $3/25$ for drag force $f=0.1$ and three values of noise strength $D=0$ (zero-noise limit), $0.02$, and $0.05$. Insets illustrate basic stable clusters of size $n_{\rm b}$ in a single well of the tilted sinusoidal potential.
• Figure 2: Phase diagram of jammed (red) and current-carrying phase (green) for two drag forces (a) $f=0.1$ and (b) $f=1$. At the transition (dotted line), the particle density equals the critical value $\rho_{\rm c}=\rho_{\rm c}(\sigma,f)$, where the dependence on $\sigma$ and $f$ is via $n_{\rm b}=n_{\rm b}(\sigma,f)$ in Eq. \ref{['eq:rhoc']}. How $n_{\rm b}=n_{\rm b}(\sigma,f)$ and $\lceil n_{\rm b}\sigma\rceil$ vary with $\sigma$ is shown in the insets for the two $f$ values. In the dark green parts of the current-carrying phases, the current increases linearly with $\rho$. At the border between the dark and bright green areas the particle density is $\rho_\ast=\rho_{\rm c}+1/\lceil n_{\rm b}\sigma\rceil^2$. The white region marks a forbidden domain, as $\rho \leq 1/\sigma$ must be satisfied.
• Figure 3: Phase diagram of jammed (red) and current-carrying phase (green) for fixed particle diameter $\sigma=3/25$. The critical density $\rho_{\rm c}=\rho_{\rm c}(\sigma,f)$ at the transition (dotted lines) decreases in a step-wise manner with increasing $f$ due to the decrease of $n_{\rm b}$ with $f$ (compare also data in the two insets of Fig. \ref{['fig:phase-diagrams-fixed-f']}). As in Fig. \ref{['fig:phase-diagrams-fixed-f']}, the current increases linearly with $\rho$ in dark green areas, while beyond the border at $\rho_\ast=\rho_{\rm c}+1/\lceil n_{\rm b}\sigma\rceil^2$ the behavior becomes nonlinear.
• Figure 4: Transition between KPZ and EW universality classes for correlations between current fluctuations. Parameters used are $\sigma=1/4$, $f=0.1$, and $D=0.05$. (a) Second derivative $J"(\rho)$ of the current-density relation shown in Fig. \ref{['fig:J-rho']}(b). (b) Correlation function $C(t)$ of current density fluctuations [Eq. \ref{['eq:C']}] for $\rho=3.3$. The dashed and solid lines are least-squares fits of power laws $C(t)=-C_\alpha t^{-\alpha}$ to the simulated data in the time range $10-10^3$ for fixed exponents $\alpha=4/3$ and $3/2$. (c) Same as (b) for $\rho=3.05$, but with dashed and solid lines corresponding to exponents $\alpha=3/2$ and 4/3.