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

@article{Ramaswamy2002ActiveNO, title={Active nematics on a substrate: Giant number fluctuations and long-time tails}, author={Sriram Ramaswamy and R. Aditi Simha and John Toner}, journal={EPL}, year={2002}, volume={62}, pages={196-202} }

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 $\sim t^{-d/2}$in the autocorrelation of the particle velocities despite the absence of a hydrodynamic velocity field. Our predictions can be tested in…

## 215 Citations

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- 2013

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- 2006

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- 2010

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- PhysicsPhysical review letters
- 2020

It is shown that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation rate for angular fluctuations, not parallel to the ordering direction, at zero wave number.

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### UCSB (NSF Grant PHY99-07949) for partial support. JT acknowledges support from NSF grant #DMR-9980123

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