Dresden 2026 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

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

DY 44.8: Poster

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

Dynamics of Aligning Active Matter: Mapping to a Schrödinger Equation and Exact Diagonalization — •Tara Steinhöfel, Horst-Holger Boltz, and Thomas Ihle — University Greifswald, Institute for Physics, Greifswald

We investigate models of Viscek-like particles with long-ranged interactions subject to noise and alignment interactions of polar and nematic symmetries. It is shown how the relevant N-particle Fokker–Planck equation can be mapped onto a Schrödinger equation in imaginary time for arbitrary particle numbers. Focusing on the minimal case of N=2, we construct a complete eigenbasis by exact diagonalization of the corresponding self-adjoint Hamiltonian. In a treatment formally equivalent to standard quantum mechanics, this yields the fully time-resolved relaxation of the N-particle-probability density from arbitrarily correlated initial conditions into the stationary state. By marginalization, the one-particle angular modes which include the usual hydrodynamic modes are obtained; we discuss their relaxation backed by agent-based simulations and give comparisons for the resulting exact relaxation rates to mean-field and to predictions from approximate field theories (G. Spera, C. Duclut, M. Durand, J. Tailleur, PRL 132, 078301 (2024)). Furthermore, we discuss possible extensions of the method to N≥ 3 particles, as well as modifications due to non-reciprocal interactions.

Keywords: Self-propelled particles; Fokker-Planck equation; Schrödinger equation; Exact Diagonalization; Stochastic Dynamics