Arrival Times in a Zero-Range Process with Injection and Decay

TL;DR

This paper derives explicit formulas for particle arrival times in a one-dimensional Zero-Range Process with injection and decay, analyzing how injection and evaporation influence particle dynamics under different rules.

Contribution

It provides exact solutions for bulk dynamics and single-site surface dynamics in ZRP, and compares simulation with steady-state approximations for multisite surface dynamics.

Findings

Exact solutions for bulk dynamics case.

Comparison of simulations with steady-state approximations.

Highlighting the impact of injection and evaporation on arrival times.

Abstract

Explicit expressions for arrival times of particles moving in a one-dimensional Zero-Range Process (ZRP) are computed. Particles are fed into the ZRP from an injection site and can also evaporate from anywhere in the interior of the ZRP. Two dynamics are considered; bulk dynamics, where particle hopping and decay is proportional to the numqber of particles at each site, and surface dynamics, where only the top particle at each site can hop or evaporate. We find exact solutions in the bulk dynamics case and for a single-site ZRP obeying surface dynamics. For a multisite ZRP obeying surface dynamics, we compare simulations with approximations obtained from the steady-state limit, where mean interarrival times for both models are equivalent. Our results highlight the competition between injection and evaporation on the arrival times of particles to an absorbing site.