51. Hydrodynamic theory of flocking in the presence of quenched disorder
- Author
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John Toner, Yuhai Tu, and Nicholas Guttenberg
- Subjects
Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed matter physics ,High Energy Physics::Lattice ,Active particles ,FOS: Physical sciences ,Order (ring theory) ,Collective motion ,Condensed Matter - Soft Condensed Matter ,Condensed Matter::Disordered Systems and Neural Networks ,01 natural sciences ,Power law ,010305 fluids & plasmas ,0103 physical sciences ,Soft Condensed Matter (cond-mat.soft) ,Polar ,010306 general physics ,Hydrodynamic theory ,Flocking (texture) ,Condensed Matter - Statistical Mechanics ,Noise (radio) - Abstract
The effect of quenched (frozen) orientational disorder on the collective motion of active particles is analyzed. We find that, as with annealed disorder (Langevin noise), active polar systems are far more robust against quenched disorder than their equilibrium counterparts. In particular, long ranged order (i.e., the existence of a non-zero average velocity $\langle {\bf v} \rangle$) persists in the presence of quenched disorder even in spatial dimensions $d=3$, while it is destroyed even by arbitrarily weak disorder in $d \le 4$ in equilibrium systems. Furthermore, in $d=2$, quasi-long-ranged order (i.e., spatial velocity correlations that decay as a power law with distance) occurs when quenched disorder is present, in contrast to the short-ranged order that is all that can survive in equilibrium. These predictions are borne out by simulations in both two and three dimensions., 22 pages, 6 figures. The long paper on flocking with quenched noise
- Published
- 2018