# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 23: Statistical Physics: General II

### DY 23.3: Vortrag

### Dienstag, 28. März 2023, 14:30–14:45, ZEU 250

**The orientation field generated by a moving defect: multivalued solutions of the diffusion equation** — •Jacopo Romano, Benoit Mahault, and Ramin Golestanian — Max Planck Institute for Dynamics and Self-Organization

Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of defects induces a long-range perturbation of the orientation landscape around them. Their effective dynamics is thus generally described in terms of quasi-particles interacting through the orientation field they produce, which in the simplest setting is described by the diffusion equation. Due to the multivaluedness of the orientation field, its expression for a defect moving with an arbitrary trajectory cannot be obtained via simple techniques and is often approximated by that of a static defect. Here, we propose a solution to this problem that relies on particular gauge invariance properties of the proper multivalued field derivatives. Our approach allows to derive the exact expression for the orientation created by multiple moving defects, which we find to depend on their past trajectories and thus to be nonlocal in time. Performing various expansions in relevant regimes, we show how improved approximations with respect to the static defect solution can be obtained. Moreover, our results lead to so far unnoticed structures in the orientation field of moving defects which we discuss in light of existing experimental results.