Direction reversing active Brownian particle in a harmonic potential.

Area of Science:

• Soft Matter Physics
• Statistical Mechanics
• Non-Equilibrium Systems

Background:

• Active Brownian particles exhibit complex dynamics due to self-propulsion and rotational diffusion.
• Confining potentials, like harmonic traps, influence the spatial distribution of active particles.
• Directional reversals introduce intermittent behavior, further modifying steady-state properties.

Purpose of the Study:

• To investigate the steady-state positional distributions of a driven active Brownian particle in a 2D harmonic trap.
• To identify and characterize distinct phases arising from the interplay of rotational diffusion, reversal rate, and trap strength.
• To analytically and numerically explore the phase transitions and their underlying mechanisms.

Main Methods:

• Analytical calculations of steady-state distributions in limiting cases.
• Characterization of phase shapes: annular, Mexican hat-like, and centrally peaked (Boltzmann and non-Boltzmann).
• Numerical simulations to complement analytical findings and construct a qualitative phase diagram.

Main Results:

• Four distinct phases (active-I/II, passive-I/II) were identified based on the shape of the positional distribution.
• Active-I: Annular distribution; Active-II: Mexican hat-like distribution with a central peak.
• Passive-I: Boltzmann-like central peak; Passive-II: Non-Boltzmann central peak with origin divergence.
• A phase transition from active-II to passive-II occurs at $\mu = \gamma$ for $D_R \ll \gamma$.

Conclusions:

• The interplay between particle activity, diffusion, and confinement leads to rich phase behavior.
• Analytical and numerical methods reveal distinct steady-state distributions and phase transitions.
• A qualitative phase diagram maps the observed phases in parameter space ($D_R$, $\gamma$, $\mu^{-1}$).