Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 44: Poster: Active Matter, Soft Matter, and Fluids

DY 44.5: Poster

Wednesday, March 11, 2026, 15:00–18:00, P5

Stochastic Path Integral for the Active Brownian Particle in a Harmonic Potential — •Mike Brandt¹, Carsten Littek², and Falko Ziebert¹ — ¹Institut für Theoretische Physik Philosophenweg 19, D-69120 Heidelberg, Germany — ²Institut für Theoretische Physik Philosophenweg 12, D-69120 Heidelberg, Germany

We present a path-integral approach for the motion of active particles in harmonic traps, developed in our recent preprint [arXiv:2509.26296]. We apply the Martin-Siggia-Rose formalism to the overdamped Langevin equations of an active Brownian particle (ABP). The associated action can be separated into an exactly solvable passive reference motion and an "activity operator" to be treated perturbatively. This method allows for the calculation of the exact, time-dependent correlation functions for the ABP in a harmonic potential. Furthermore, the probability density can be perturbatively expanded in a series, which already captures important qualitative features of the system at low orders. This is exemplified by discussing the transition between a ring-shaped distribution for a weak potential and a peaked distribution for a strong potential in the long-time limit. Finally, we present full time-dependent expressions for the mean-square displacement of the Brownian circle swimmer (BCS), along with comparisons to simulations.

Keywords: Active Brownian Particle; Stochastic Path Integral; Brownian Circle Swimmer