Universal dynamics of a passive particle driven by Brownian motion

Area of Science:

• Statistical physics
• Soft matter physics
• Nonlinear dynamics

Background:

• Investigating particle dynamics in complex systems is crucial for understanding phenomena from molecular motors to active matter.
• Nonreciprocal interactions introduce unique behaviors not seen in equilibrium systems.
• Brownian motion serves as a fundamental model for random processes.

Purpose of the Study:

• To analyze the overdamped dynamics of a passive particle driven by a Brownian particle via nonreciprocal interactions.
• To determine the universality of the driven particle's long-time behavior.
• To compute exact scaling functions for position distribution in one and two dimensions.

Main Methods:

• Theoretical analysis of overdamped Langevin equations.
• Focus on short-range and long-range interaction potentials.
• Calculation of mean-squared displacement (MSD) and position distributions.
• Dimensional analysis in 1D and 2D spatial dimensions.

Main Results:

• For short-range interactions, the driven particle's MSD exhibits universal behavior, growing as t^{1/2} in 1D and log(t) in 2D.
• Exact scaling functions for position distribution are computed and found to be universal for short-range interactions.
• For long-range interactions, the MSD exponent depends on the potential's tail properties.

Conclusions:

• The long-time dynamics of a passively driven particle are remarkably universal for short-range nonreciprocal interactions.
• The specific form of the potential becomes irrelevant for short-range interactions, simplifying predictions.
• The study provides exact scaling functions, offering deeper insights into driven Brownian systems.