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

Abstract

We study the response of probe particles to weak constant driving in kinetically constrained models of glassy systems, and show that the probe's response can be non-monotonic and give rise to negative differential mobility: increasing the applied force can reduce the probe's drift velocity in the force direction. Other significant non-linear effects are also demonstrated, such as the enhancement with increasing force of the probe's fluctuations away from the average path, a phenomenon known in other contexts as giant diffusivity. We show that these results can be explained analytically by a continuous-time random walk approximation where there is decoupling between persistence and exchange times for local displacements of the probe. This decoupling is due to dynamic heterogeneity in the glassy system, which also leads to bimodal distributions of probe particle displacements. We discuss the relevance of our results to experiments.

Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments

“…It coincides with that of Ref. [41], but the transition rates in the transverse direction with respect to the field can have different expressions, as considered for instance in [40,43]. The theoretical treatment proposed in the following is however general and does not rely on a specific form of p ν .…”

“…This remarkable "getting more from pushing less" behavior [46] occurs not only in lattice models, but it is observed in several systems, such as nonequilibrium steady states [46], Brownian motors [47,48], and kinesin models [49]. In particular, in the context of kinetically constraint models, NDM has been observed in numerical simulations in [40,50] and related to the heterogeneity and intermittency of the dynamics in the glassy phase [40]. More recently, an analytical theory accounting for NDM in a Lorentz lattice gas, where the TP travels among fixed obstacles, has been presented by Leitmann and Franosch [41] in the dilute limit (i.e.…”

“…Recently, the behavior of V (F ) beyond the linear regime in lattice gas models has received great attention, triggered by the observation of the striking phenomenon of negative differential mobility (NDM), namely a nonmonotonic dependence of the TP velocity on the applied force [39][40][41][42][43][44][45]. Upon a gradual increase of the force F , the velocity grows linearly, as prescribed by the linear response, then approaches a maximal value and further decreases with an increase of F .…”

Microscopic Theory for Negative Differential Mobility in Crowded Environments

“…Such a counter-intuitive "getting more from pushing less" [17] behavior of the differential mobility (or of the differential conductivity) has been observed for a variety of physical systems and processes, e.g. for electron transfer in semiconductors at low temperatures [18][19][20][21], hopping processes in disordered media [22], transport of electrons in mixtures of atomic gases with reactive collisions [23], far-from-equilibrium quantum spin chains [24], some models of Brownian motors [25,26], soft matter colloidal particles [27], different nonequilibrium systems [17], and also for the kinetically constrained models of glass formers [28][29][30].Apart of these examples, negative differential mobility (NDM) has been observed in the minimal model of a driven lattice gas, which captures many essential features of the behavior in realistic systems. In this model one focuses on the dynamics of a hard-core tracer particle (TP) …”

Microrheology of supercooled liquids in terms of a continuous time random walk

“…Under application of the force, the jumping directions become biased so that one gets for the average displacement ∆x = a 0 tanh a 0 2 βF . This particular ansatz was further discussed by Jack et al 20 . By linear expansion, Eq.…”