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We study the response of probe particles to weak constant driving inkinetically constrained models of glassy systems, and show that the probe'sresponse can be non-monotonic and give rise to negative differential mobility:increasing the applied force can reduce the probe's drift velocity in the forcedirection. Oth er significant non-linear effects are also demonstrated, such asthe enhancement with increasing force of the probe's fluctuations away from theaverage path, a phenomenon known in other contexts as giant diffusivity. Weshow that these res ults can be explained analytically by a continuous-timerandom walk approximatio n where there is decoupling between persistence andexchange times for local dis placements of the probe. This decoupling is due todynamic heterogeneity in the glassy system, which also leads to bimodaldistributions of probe particle disp lacements. We discuss the relevance of ourresults to experiments.

Negative differential mobility of weakly driven particles in models of glass formers