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

¹ Centre for Condensed-Matter Theory, Department of Physics Indian Institute of Science - Bangalore 560 012, India
² Department of Physics, University of Oregon - Eugene, OR 94703, USA

Corresponding authors: sriram@physics.iisc.ernet.in, aditi@mpipks-dresden.mpg.de, jjt@darkwing.uoregon.edu

Received: 27 August 2002
Accepted: 18 February 2003

Abstract

We construct the equations of motion for the coupled dynamics of order parameter and concentration for the nematic phase of driven particles on a solid surface, and show that they imply i) giant number fluctuations, with a standard deviation proportional to the mean in dimension d = 2 of primary relevance to experiment, and ii) long-time tails in the autocorrelation of the particle velocities despite the absence of a hydrodynamic velocity field. Our predictions can be tested in experiments on aggregates of amoeboid cells as well as on layers of agitated granular matter.