Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations

Abstract

We extend recent results on the exact hydrodynamics of a system of diffusive active particles displaying a motility-induced phase separation to account for typical fluctuations of the dynamical fields. By calculating correlation functions exactly in the homogeneous phase, we find that two macroscopic length scales develop in the system. The first is related to the persistence length of the particles and the other to the collective behavior of the particles. The latter diverges as the critical point is approached. Our results show that the critical behavior of the model in one dimension belongs to the universality class of a mean-field Ising model, both for static and dynamic properties, when the thermodynamic limit is taken in a specified manner. The results are compared to the critical behavior exhibited by the ABC model. In particular, we find that in contrast to the ABC model the density large deviation function, at its Gaussian approximation, does not contain algebraically decaying interactions but is of a finite, macroscopic, extent which is dictated by the diverging correlation length.

Active Random Walks in One and Two Dimensions

“…Lattice models of interacting particle systems have also been used as paradigmatic models to study the non-trivial collective effects associated with dense particulate matter [55,56]. It has recently been shown that phase transitions resem-bling Motility Induced Phase Separation can be realized in lattice models with activity [15,57], however with microscopic rules different from our case. It would therefore be interesting to generalize our study to interacting active lattice walks to better understand the nature of the non-equilibrium phases that appear in collections of active particles.…”

Long-range influence of a pump on a critical fluid

“…They are known to generically exhibit a motility-induced phase separation [10][11][12][13][14][15][16][17][18][19][20][21][22][23] as a function of the density and the selfpropulsion strength of the active particles. While the behavior at the critical point has been under some debate, field theoretical arguments suggest that the terms which break time reversal symmetry are irrelevant at the critical point so that the system belongs to the Ising universality class [24][25][26][27][28]. Interestingly, these systems can be pumped by introducing a passive asymmetric object rather than a pump [29][30][31][32][33][34].…”