Inertial self-propelled particles.

Area of Science:

• Physics
• Soft Matter Physics
• Statistical Mechanics

Background:

• Self-propelled particles (SPPs) are crucial in various fields, from biological systems to synthetic materials.
• Understanding SPP behavior in viscous media requires accounting for inertial effects, often neglected in simpler models.

Purpose of the Study:

• To investigate the influence of inertia on the dynamics and statistical properties of underdamped active Ornstein-Uhlenbeck particles.
• To analyze correlations between position, velocity, and self-propulsion forces in non-equilibrium steady states.
• To examine the impact of inertia on virial pressure and correlation functions.

Main Methods:

• Employing the underdamped active Ornstein-Uhlenbeck model for theoretical analysis.
• Studying both potential-free and harmonically confined particle systems.
• Calculating correlation matrices and steady-state probability distributions.

Main Results:

• Identified significant equal-time correlations between particle velocity and active force in the non-equilibrium steady state.
• Observed inertia-induced non-monotonic decay in position and velocity two-time correlation functions.
• Quantified changes in virial pressure when transitioning from overdamped to underdamped regimes.

Conclusions:

• Inertia plays a critical role in shaping the dynamics and statistical mechanics of active matter systems.
• The underdamped active Ornstein-Uhlenbeck model provides a framework for understanding complex correlations and pressure effects.
• Results extend to interacting active particle chains, highlighting broader applicability.