Abstract
Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond ℓ_{r}, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured. Below ℓ_{r}, nematic order is long-range. We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics. We check numerically our theoretical predictions, in particular the presence of π-symmetric propagative sound modes, and provide estimates of all scaling exponents governing long-range space-time correlations.
Highlights
Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond lr, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured
We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics
In spite of all this progress, important fundamental questions remain open. Such a longstanding issue is whether true long-range nematic order can emerge in two space dimensions (2D). Whereas it is well known, notably thanks to the seminal work by Toner and Tu, that long-range polar order can arise in 2D active systems [26,27,28,29,30,31,32,33,34], the debate has remained open for active nematics: On the one hand, theoretical results conclude that nematic order can at best be quasi-long-range [35], as in equilibrium, albeit with important differences [37,38,39,40,41,42,43]
Summary
Whereas it is well known, notably thanks to the seminal work by Toner and Tu, that long-range polar order can arise in 2D active systems [26,27,28,29,30,31,32,33,34], the debate has remained open for active nematics: On the one hand, theoretical results conclude that nematic order can at best be quasi-long-range [35], as in equilibrium, albeit with important differences [37,38,39,40,41,42,43]. Long-Range Nematic Order in Two-Dimensional Active Matter Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond lr, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured.
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