Generalized Ornstein-Uhlenbeck model for active motion.

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Active matter systems exhibit complex dynamics driven by self-propulsion.
• Generalized Langevin equations (GLEs) are crucial for modeling systems with memory effects.
• The active Ornstein-Uhlenbeck (OU) model provides a baseline for active particle dynamics.

Purpose of the Study:

• To investigate a one-dimensional model of active motion incorporating persistent self-propulsion via memory functions.
• To generalize the active Ornstein-Uhlenbeck model by including exponential and power-law memory kernels.
• To analyze the influence of different memory types and colored noise on particle dynamics.

Main Methods:

• Development of a generalized Langevin equation with a memory function for particle swimming velocity.
• Inclusion of exponential decay and power-law memory functions.
• Addition of colored noise to the system.
• Derivation of analytical expressions for the velocity autocorrelation function and mean-squared displacement.
• Validation of analytical results through numerical simulations.

Main Results:

• Analytical expressions for velocity autocorrelation and mean-squared displacement were derived and validated by simulations.
• Damped oscillatory solutions were observed for both exponential and power-law memory models.
• The competition between system memory and persistent velocity fluctuations drives the oscillatory behavior.
• Active subdiffusion was demonstrated for the power-law memory model with fractional Brownian noise, especially with increasing long-term memory.

Conclusions:

• The proposed generalized Langevin equation model effectively captures active particle dynamics with memory.
• Memory effects significantly influence particle trajectories, leading to damped oscillations and subdiffusion.
• Long-term memory, particularly in power-law models, promotes active subdiffusion, a key finding for understanding anomalous transport in complex systems.