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Direct Imaging of Laser-driven Ultrafast Molecular Rotation

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Direction reversing active Brownian particle in a harmonic potential.

Ion Santra¹, Urna Basu^1,2, Sanjib Sabhapandit¹

¹Raman Research Institute, Bengaluru 560080, India.

|November 2, 2021

Summary

We identified four distinct phases in active Brownian particle motion within a harmonic trap, driven by rotational diffusion, reversal rate, and trap strength. These phases, active-I/II and passive-I/II, exhibit unique positional distributions.

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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 ($D_R$, $\gamma$, $\mu^{-1}$).