Path integral description of semiflexible active Brownian polymers

Area of Science:

• Soft Matter Physics
• Polymer Physics
• Statistical Mechanics

Background:

• Semiflexible polymers composed of active Brownian particles (ABPOs) display complex behaviors driven by internal activity.
• Existing mean-field theories, like the Gaussian semiflexible polymer model, offer insights but may not capture all activity-induced effects.

Purpose of the Study:

• To derive a path integral representation for the stationary-state distribution function of ABPOs.
• To investigate the influence of activity-dependent coefficients and contour correlations on ABPO conformations.
• To compare the path integral results with full solutions and understand the role of colored noise.

Main Methods:

• Derivation of a path integral formulation for ABPOs based on Langevin dynamics.
• Analysis of normal mode amplitudes and their stationary-state distributions.
• Calculation of polymer properties like tangent-vector correlation and mean-square end-to-end distance within a semiflexible approximation.

Main Results:

• The path integral successfully incorporates semiflexible polymer contributions (entropy, bending energy) and activity-induced correlations (torsional, higher order).
• The mean-square end-to-end distance shows good agreement with full solutions for higher activities, particularly for flexible polymers.
• The approximation highlights the significance of torsional and higher-order contour correlations in determining ABPO conformations.

Conclusions:

• The derived path integral provides a powerful tool for analyzing the conformational properties of ABPOs.
• Active fluctuations (colored noise) significantly alter semiflexible polymer conformations compared to passive thermal fluctuations (white noise).
• The study underscores the importance of considering higher-order contour correlations for a comprehensive understanding of active polymer behavior.