Active nematics on a substrate: Giant number fluctuations and long-time tails

Abstract

We construct the equations of motion for the coupled dynamics of order\nparameter and concentration for the nematic phase of driven particles on a\nsolid surface, and show that they imply (i) giant number fluctuations, with a\nstandard deviation proportional to the mean and (ii) long-time tails $\\sim\nt^{-d/2}$ in the autocorrelation of the particle velocities in $d$ dimensions\ndespite the absence of a hydrodynamic velocity field. Our predictions can be\ntested in experiments on aggregates of amoeboid cells as well as on layers of\nagitated granular matter.\n