Arrival times in a zero-range process with injection and decay

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 evaporate from any site of the one-dimensional lattice. Two dynamics are considered: bulk dynamics, where particle hopping and decay are proportional to the number 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 in the arrival times of particles to an absorbing site. PACS numbers: 05.60.−k, 87.16.Ac, 05.10.Ln (Some figures in this article are in colour only in the electronic version)