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We consider the propagation of a single particle in a random chain, assistedby the coupling to dispersive bosons. Time evolution treated with rateequations for hopping between localized states reveals a qualitative differencebetween dynamics due to noninteracting bosons and hard-core bosons. In thefirst case the transient dynamics is subdiffusive, but multi-boson processesallow for long-time normal diffusion, while hard-core effects suppressmulti-boson processes leading to persistent subdiffusive transport, consistentwith numerical results for a full many-body evolution. In contrast, analogousstudy for a quasiperiodic potential reveals a stable long-time diffusion.

Transient and persistent particle subdiffusion in a disordered chain coupled to bosons