Active Brownian ring polymers

The conformational and dynamical properties of semiflexible active Brownian ring polymers are investigated analytically. A ring is described by the Gaussian semiflexible polymer model accounting for the finite contour length. Activity is implemented by a Gaussian, non-Markovian stochastic process resembling either an external nonthermal force or a local self-propulsion velocity as for an active Ornstein-Uhlenbeck particle. Specifically, the fluctuation spectrum of normal-mode amplitudes is analyzed. At elevated activities, flexible (tension) modes dominate over bending modes even for semiflexible rings, corresponding to enhanced conformational fluctuations. The fluctuation spectrum exhibits a crossover from a quadratic to a quartic dependence on the mode number with increasing mode number, originating from intramolecular tension, but the relaxation behavior is either dominated by intra-polymer processes or the active stochastic process. A further increase in activity enhances fluctuations at large length scales at the expense of reduced fluctuations at small scales. Conformationally, the mean square ring diameter exhibits swelling qualitatively comparable to liner polymers. The ring's diffusive dynamics is enhanced, and the mean square displacement shows distinct activity-determined regimes, consecutively, a ballistic, a subdiffusive, and a diffusive regime. The subdiffusive regime disappears gradually with increasing activity.