Segregation at a single trap in the presence of fields

There have been a number of recent investigations of segregation properties of diffusing particles in the presence of a single static trap in low dimensions. We study these properties when the diffusing particles are subject to different forms of external fields: global constant bias, random bias fields (Sinai model) and random transition rates. We discuss two measures of segregation, the distances from the trap either to the point at which the concentration profile reaches a specified fraction of its bulk value, or to the nearest unreacted particle. For the cases of global bias (both away from, and towards the trap) and random fields, we found that both measures of segregation have the same asymptotic temporal behavior, while for random transition rates they differ. We explain this difference by relating the nearest-neighbor distance measure to properties of hardcore diffusion in these systems. We also found anomalous spatial shapes for the profile in the vicinity of the trap in the random systems, as well as anomalous reaction rates.