Particle transport at arbitrary timescales with Poisson-distributed collisions.

Area of Science:

• Physics
• Statistical Mechanics
• Stochastic Processes

Background:

• Random walkers are fundamental models in physics.
• Understanding transport properties is crucial in various scientific fields.
• Previous models often simplify collision dynamics.

Purpose of the Study:

• To model the time evolution of a persistent random walker's position and variance.
• To investigate the impact of Poisson-distributed collisions on transport properties.
• To analyze the influence of different velocity transition functions.

Main Methods:

• Developed a mathematical model for a random walker with velocity changes upon collision.
• Incorporated Poisson-distributed collisions at a constant rate.
• Studied three distinct velocity transition functions.
• Analyzed transport properties through the evolution of the variance.

Main Results:

• The model captures the time evolution of mean location and variance.
• Observed that transport properties can change their character over time.
• Early-time behavior of the walker is sensitive to initial conditions.
• Different velocity transition functions lead to varied transport characteristics.

Conclusions:

• The study provides insights into the complex dynamics of random walkers under intermittent velocity changes.
• Highlights the importance of considering time-dependent transport and initial conditions.
• The developed model offers a framework for studying similar stochastic systems.