Anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes

TL;DR

This study investigates anomalous diffusion behaviors in generalized asymmetric exclusion models with particles of various sizes, revealing KPZ universality and extending theoretical predictions to negative particle sizes through numerical and analytical methods.

Contribution

It introduces a generalized exclusion model with particles of arbitrary sizes, demonstrating KPZ universality and extending Bethe-ansatz calculations to negative sizes.

Findings

Correlation functions grow as t^{1/3}, indicating KPZ universality.

The dynamical critical exponent z=3/2 is confirmed for all particle sizes.

Anomalous diffusion persists regardless of the interaction range.

Abstract

Anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem. In these generalized models the range of the hard-core interactions are changed and the restriction of relative ordering of the particles is partially brocken. The models probing these effects are those of biased diffusion of particles having size S=0,1,2,..., or an effective negative "size" S=-1,-2,..., in units of lattice space. Our numerical simulations show that irrespective of the range of the hard-core potential, as long some relative ordering of particles are kept, we find suitable sliding-tag correlation functions whose fluctuations growth with time anomalously slow ($t^{{1/3}}$), when compared with the normal diffusive behavior ($t^{{1/2}}$). These results indicate that the critical behavior of these stochastic models are in the Kardar-Parisi-Zhang (KPZ) universality class. Moreover a previous Bethe-ansatz calculation of the dynamical critical exponent $z$, for size $S \geq 0$ particles is extended to the case $S<0$ and the KPZ result $z=3/2$ is predicted for all values of $S \in {Z}$.