Fluctuating nonlinear hydrodynamics of flocking.

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Active matter systems exhibit complex collective behaviors.
• Continuum field theories are often used to describe these systems.
• The derivation of macroscopic equations from microscopic models is crucial for understanding emergent phenomena.

Purpose of the Study:

• To present a continuum field theoretic description of active particle system dynamics.
• To derive equations of motion for collective densities from single-particle dynamics.
• To obtain coarse-grained equations of fluctuating nonlinear hydrodynamics (FNH) and determine their transport coefficients.

Main Methods:

• Starting from a microscopic model of active particles.
• Deriving exact equations of motion for collective densities of mass and momentum.
• Averaging over a local equilibrium distribution to obtain coarse-grained FNH equations.
• Determining transport coefficients from microscopic parameters.

Main Results:

• Exact derivation of collective density equations from single-particle dynamics.
• Identification of noise and anomalous momentum dependence in single-particle friction.
• Obtained coarse-grained fluctuating nonlinear hydrodynamics (FNH) equations.
• Transport coefficients in FNH are explicitly linked to microscopic model parameters.

Conclusions:

• The study provides a rigorous microscopic foundation for fluctuating nonlinear hydrodynamics in active systems.
• It demonstrates how macroscopic transport properties emerge from microscopic details.
• This work bridges the gap between microscopic descriptions and macroscopic continuum theories for active matter.