Role of trapping and crowding as sources of negative differential mobility

Increasing the crowding in an environment does not necessarily trigger negative differential mobility of strongly pushed particles. Moreover, the choice of the model, in particular the kind of microscopic jump rates, may be very relevant in determining the mobility. We support these points via simple examples and we therefore address recent claims saying that crowding in an environment is likely to promote negative differential mobility. Trapping of tagged particles enhanced by increasing the force remains the mechanism determining a drift velocity not monotonous in the driving force.