Quenched Disorder-Induced Mobility Decrease with Increasing Channel Width

We study the diffusion of a tracer particle with stochastic dynamics confined to a narrow channel while a constant external pulling force is applied. We show that for such geometry, the presence of strong quenched disorder leads to a counterintuitive behavior: the mobility of the particle decreases as the channel width grows. Such an effect only arises when the quenched disorder is sufficiently strong and the diffusion is anomalous. We present a theoretical basis that predicts and explains this effect. The mean position in the presence of a strong quenched disorder is found to have a complex non-linear dependence on the force which results in breaking of the Einstein relation.