ısica da Mat´ria Condensada / ID: 422-3
XXX Encontro Nacional de F´ e 1
Active nematics: quasi-long-range order and giant ﬂuctuations
Hugues Chat´, Francesco Ginelli
CEA - Service de Physique de l’Etat Condens´, Saclay, France
ısica Te´rica e Experimental, Universidade Federal do Rio Grande do Norte, Natal-RN
Departamento de F´ o
Physicists have been looking for common, possibly universal, features of the collective motion of animals,
bacteria, cells, molecular motors, as well as driven granular objects [1, 2]. Among the emergent properties
of these groups of active or self-propelled particles (SPP), distinctively out-of-equilibrium features have been
found, such as the existence of long-range orientational order in two-dimensional ferromagnetic ﬂocks of polar
Another set of striking intrinsically nonequilibrium properties have recently been predicted by Ramaswamy
and co-workers . They considered, in particular, the case of apolar but oriented SPP and argued that such
active nematics should diﬀer dramatically from the usual (equilibrium) case. In particular, their approach,
based on the analysis of hydrodynamic equations derived from symmetry arguments, predicts that giant density
ﬂuctuations arise in the ordered phase of such media. In, it is also hinted at the possibility of true long-range
order and of a diﬀerent isotropic-nematic transition out of equilibrium, but no deﬁnitive statement is oﬀered.
Resolving these issues is nevertheless crucial, especially in view of the predicted giant density ﬂuctuations, and
all the more so since, in polar SPP, the transition to true long-range order was shown to be discontinuous
A minimal microscopic model is proposed  for active nematic particles similar in spirit to the Vicsek model
for self-propelled polar particles. In two dimensions, we show that this model exhibits a Kosterlitz-Thouless-like
transition to quasi-long-range orientational order and that in this non-equilibrium context, the ordered phase
is characterized by giant density ﬂuctuations.
 John Toner, Yuhai Tu, and Sriram Ramaswamy. Hydrodynamis and phases of ﬂocks. Annals of Physics,
 Igor S. Aranson and Lev S. Tsimring. Patterns and collective behavior in granular media: Theoretical
concepts. Rev. of Modern Phys., 78:641, 2006.
 Hughes Chat´, Francesco Ginelli, and Raul Montagne. Simple model for active nematics: Quasi-long-range
order and giant ﬂuctuations. Phys. Rev. Lett., 96:180602, 2006.