Diffusion transitions induced by shear-thinning viscosity: application to laser-cooled atomic gases

Abstract

We study the diffusive dynamics of a system in a nonlinear velocity-dependent frictional environment within a continuous time random walk model. In this model, the motion is governed by a shear-thinning frictional force, $-\gamma_0v/[1+(v^2/v_{\mathrm{c}}^2)]^\mu$ ( $0\lt\mu\unicode{x2A7D}1$ ), where γ _0 represents the coefficient of static friction and µ is the scaling index. Through analytical and numerical results, we construct a diffusion phase diagram that encompasses different regimes upon variations in parameters γ _0 and µ : normal diffusion; superdiffusion; and hyperdiffusion. These transitions occur because the induced weaker friction enhances the diffusion. With a decrease in the scaling index, we find that the γ _0 -dependent exponent of diffusion converges towards the experimental findings for ultracold ^87 Rb atoms because the strong effective friction arises. The discrepancies between the fractional Lévy kinetics and the experimental findings may be potentially reconciled. We believe that these findings are helpful for analyzing experimental observations of cold atoms diffusing in optical lattices.

Keywords

• diffusion transitions
• anomalous viscoelastic dynamics
• shear-thinning viscosity
• cold atoms
• continuous-time random walk