Harmonically trapped inertial run-and-tumble particle in one dimension

Area of Science:

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

Background:

• Active matter systems exhibit complex dynamics far from equilibrium.
• Inertia's role in active particle behavior is crucial but not fully understood.
• Run-and-tumble models capture essential features of biological motility.

Purpose of the Study:

• To analyze the nonequilibrium stationary state of a 1D inertial run-and-tumble particle (IRTP) in a harmonic potential.
• To characterize the influence of inertia on particle dynamics and phase space confinement.
• To investigate how inertial and active timescales affect position and velocity fluctuations.

Main Methods:

• Analytical computation of phase plane confinement regions.
• Characterization of dynamical regimes (overdamped vs. underdamped) based on timescale ratios.
• Analysis of position and velocity distribution functions across different activity levels.

Main Results:

• Inertia leads to two distinct dynamical regimes: overdamped and underdamped.
• Particle confinement is restricted to specific phase plane regions in both regimes.
• Position and velocity distributions exhibit unique transitions, including multi-peaked and U-shaped forms, depending on activity and inertia.

Conclusions:

• The interplay of inertia and activity dictates the complex nonequilibrium behavior of IRTPs.
• Distinct subregimes emerge, characterized by novel fluctuation patterns.
• Understanding these dynamics is key for modeling active matter in confined environments.