Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder
File(s)
Accepted version
Author(s)
Chen, Leiming
Lee, Chiu Fan
Maitra, Ananyo
Toner, John
Type
Journal Article
Abstract
We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two
d
=
(
d
c
−
ε
)
expansions to
O
(
ε
)
, obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a “hard” continuation which has
d
c
=
7
3
, and a “soft” continuation with
d
c
=
5
2
. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and therefore we expect the numerical values that we predict for them to be highly accurate.
d
=
(
d
c
−
ε
)
expansions to
O
(
ε
)
, obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a “hard” continuation which has
d
c
=
7
3
, and a “soft” continuation with
d
c
=
5
2
. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and therefore we expect the numerical values that we predict for them to be highly accurate.
Date Issued
2022-10-27
Date Acceptance
2022-09-13
Citation
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2022, 106, pp.1-29
ISSN
1539-3755
Publisher
American Physical Society
Start Page
1
End Page
29
Journal / Book Title
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume
106
Copyright Statement
©2022 American Physical Society
Identifier
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.106.044608
Publication Status
Published
Date Publish Online
2022-10-27