Directed diffusion of reconstituting dimers

TL;DR

This paper explores the complex dynamical behavior of an asymmetric assisted diffusion model of reconstituting dimers, revealing phenomena like kinematic waves and non-ergodic effects, analyzed through analytical and numerical methods.

Contribution

It introduces a detailed analysis of the asymmetric assisted diffusion of reconstituting dimers, emphasizing the role of the irreducible string and sector-dependent mappings.

Findings

Identification of kinematic wave phenomena.

Demonstration of strongly broken ergodicity.

Analysis of asymptotic dynamics via mappings to ASEP.

Abstract

We discuss dynamical aspects of an asymmetric version of assisted diffusion of hard core particles on a ring studied by G. I. Menon {\it et al.} in J. Stat Phys. {\bf 86}, 1237 (1997). The asymmetry brings in phenomena like kinematic waves and effects of the Kardar-Parisi-Zhang nonlinearity, which combine with the feature of strongly broken ergodicity, a characteristic of the model. A central role is played by a single nonlocal invariant, the irreducible string, whose interplay with the driven motion of reconstituting dimers, arising from the assisted hopping, determines the asymptotic dynamics and scaling regimes. These are investigated both analytically and numerically through sector-dependent mappings to the asymmetric simple exclusion process.