Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 23: Poster: Active Matter, Soft Matter, Fluids (joint session DY/CPP)

DY 23.12: Poster

Wednesday, March 19, 2025, 10:00–12:00, P3

Statistical Field Theory for Vicsek-type models — •Carsten Littek, Falko Ziebert, and Matthias Bartelmann — Institut für Theoretische Physik, Universität Heidelberg, Germany

Dry, aligning, dilute active matter systems display a wide range of emergent phenomena such as collective, orientationally ordered motion and phase separation. The self-propelled particles in such systems undergo noisy aligning interactions with their neighbours, but they do not exchange momentum with their surrounding. While microscopic and hydrodynamic descriptions, whose connection involves approximations, exist, their predicted behaviour - such as scaling exponents - do not match.

Here we present a microscopic statistical field theory for active Brownian particles inspired by Mazenko (2010). In our formulation we interpret the particles’ two-dimensional positions and their direction of motion as Martin-Siggia-Rose (MSR) fields to obtain a path integral representation of the N-particle partition function. The MSR action is augmented by a two-particle interaction that aligns particle directions either ferromagnetically as in the Vicsek model or nematically. Similar to quantum many-body theory the benefit of our field theoretic formulation of Vicsek-type models is that it allows for developing a self-consistent perturbation theory and using renormalization techniques. Our aim is the calculation of density and velocity correlation functions in the homogeneous ordered phase and the transition into the ordered phase.

Keywords: Vicsek model; Statistical Field Theory; Ordered Motion; Density Correlations; Dry aligning dilute active matter