Confined run-and-tumble particles with non-Markovian tumbling statistics

Area of Science:

• Statistical Physics
• Soft Matter Physics
• Non-equilibrium Systems

Background:

• Confined active particles model complex systems reaching non-equilibrium steady states.
• Run-and-tumble particles are fundamental models in statistical physics.
• Non-Markovian dynamics arise from non-exponential waiting time distributions.

Purpose of the Study:

• Investigate the steady-state distribution (SSD) of a confined run-and-tumble particle in one dimension.
• Develop an efficient numerical method for analyzing non-Markovian active particle systems.
• Explore the relationship between SSD and large-deviation functions in the small-τ regime.

Main Methods:

• Analytical framework using effective position-dependent tumbling rates.
• Development of an efficient numerical method for calculating the steady-state distribution.
• Analysis of non-exponential waiting time distributions.

Main Results:

• A numerical method was developed to efficiently compute the full steady-state distribution (SSD).
• The method is effective even for challenging non-Markovian dynamics and small mean waiting times (τ).
• A scaling relation connects the SSD to the large-deviation function in specific regimes.

Conclusions:

• The developed numerical method provides an efficient approach to study confined active particles.
• Understanding non-Markovian effects is crucial for accurately predicting particle behavior in non-equilibrium systems.
• The findings offer insights into the statistical properties of active matter under confinement.