Resonance-like enhancement of forced nonlinear diffusion as a nonequilibrium phase transition

We describe the phenomenon of a resonance-like, giant enhancement of diffusion in a basic model of nonlinear diffusion featured by a nonlinear in velocity friction and the corresponding multiplicative thermal noise. The model is consistent with thermal equilibrium in the absence of driving. Different from previous studies of this phenomenon, where the crucial nonlinearity originates from a periodic external potential while friction is linear, we focus on the case of a constant force driving, whereas the crucial nonlinearity stems from the friction. The basic model of such friction considered interpolates between linear viscous Stokes friction at small velocities and dry Coulomb-like friction at large velocities corresponding to a stress plateau in some nonlinear viscoelastic materials. Recently, a nonequilibrium phase transition to super-diffusion and super-transport was discovered within this basic model. We show that adding a tiny viscous friction part to major nonlinear friction regularizes in part this behavior. Diffusion becomes asymptotically normal. However, the phase transition translates into a giant enhancement of normal diffusion and mobility of particles at the transition point over the intuitively expected large force limit, where the linearization of friction occurs. Such a giant enhancement of diffusion is closely related to the largely enhanced kinetic temperature of the particles at and beyond the critical point. We provide analytical results obtained within an effective mass approximation which nicely agree with stochastic numerics.