Short-range and long-range correlations in driven dense colloidal mixtures in narrow pores

TL;DR

This paper models driven dense colloidal mixtures in narrow pores using a generalized ASEP, revealing that long-range correlations decay algebraically with universal exponents, contrasting with traditional exponential decay predictions.

Contribution

It introduces a two-species, multi-particle-site generalization of ASEP and analyzes both short- and long-range correlations, highlighting different universality classes.

Findings

Nearest-neighbor correlations are accurately predicted by Kirkwood approximation.

Long-range correlations decay algebraically, not exponentially, with universal power-law exponents.

Two-species systems exhibit oscillating correlations with slow decay, indicating complex behavior.

Abstract

The system of driven dense colloid mixture in a tube with diameter comparable with particle size is modeled by a generalization of asymmetric simple exclusion (ASEP) model. The generalization goes in two directions: relaxing the exclusion constraint by allowing several (but few) particles on a site, and by considering two species of particles, which differ by size and transport coefficients. We calculate the nearest-neighbor correlations using a variant of Kirkwood approximation and show by comparison with numerical simulations that the approximation provides quite accurate results. However, for long-range correlations, we show that the Kirkwood approximation is useless, as it predicts exponential decay of the density-density correlation function with distance, while simulation data indicate that the decay is algebraic. For one-component system, we show that the decay is governed by a power law with universal exponent close to 2. In two-component system, the correlation function behaves in more complicated manner; its sign oscillates but the envelope decays again very slowly and the decay is compatible with power-law with exponent somewhat lower than 2. Therefore, our generalization of ASEP belongs to different universality class than the ensemble of generalized ASEP models which are mappable to zero-range processes.