Generalized persistence dynamics for active motion.

Area of Science:

• Statistical Physics
• Active Matter Physics
• Theoretical Physics

Background:

• Active matter exhibits persistent motion, a key characteristic challenging to model theoretically.
• Existing models often rely on explicit orientational dynamics, limiting their generality.
• Understanding active particle behavior is crucial for fields ranging from biology to materials science.

Purpose of the Study:

• To develop a general theoretical framework for the statistical physics of self-propelled particles.
• To incorporate particle persistence on an equal footing with Brownian motion.
• To analyze various active motion patterns characterized by different persistence exponents.

Main Methods:

• Developed a Smoluchowski-like equation for particle probability density without assuming explicit velocity dynamics.
• Introduced a two-time memory function, K(t,t'), to describe motion persistence.
• Focused on a specific form of the memory function: K(t,t') ~ (t/t')^{-η}exp[-Γ(t-t')].

Main Results:

• The framework successfully describes active motion patterns characterized by the exponent η.
• Derived analytical expressions for the intermediate scattering function, a key experimental observable.
• Obtained analytical expressions for the time dependence of the mean-squared displacement and kurtosis.

Conclusions:

• The proposed theoretical framework offers a robust method for analyzing self-propelled particle dynamics.
• The model accurately captures the role of persistence in active matter.
• The derived analytical results facilitate experimental validation and further theoretical exploration.