Anomalous segregation at a single trap in disordered chains

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Abstract
We study the repulsion of Brownian particles induced by a single trap on disordered chains. Two different types of disorder are considered: random local bias fields (the Sinai model) and random transition rates. We discuss two possible measures of segregation for each system, and show that they can have either similar or different universal behavior, depending on the properties of diffusion subject to the hard-core potential in each system. We also report on anomalous scaling properties for the average trapping rate and the average density profile of the diffusing particles. It is surprisingly shown that the latter is not spatially linear in the vicinity of the trap, but rather has a flat tail in the case of random fields, and a nonuniversal power-law in the case of random transition rates.