Grand Séminaire d'Institut

Vendredi 14 Juin 2024 à 11h00.

Topological defects in active XY models

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I will show how activity can dramatically affect the behaviour of topological defects in 2D planar spin systems (XY model). I will explain the impact (A) intrinsic torques à la Kuramoto (B) non-reciprocal interactions (vision cones) can have on the large scale system through the behaviour of topological defects.

I’ll start by focusing on the (short-range) noisy Kuramoto model, an active version of the equilibrium XY model. I’ll explain how the intrinsic torques impact the static and dynamic properties of defects, breaking down the celebrated Berenzinskii-Kosterlitz-Thouless (BKT) scenario. In particular, I’ll explain why intrinsic torques induce a steady self-propulsion of the defects, with an interesting mean-square displacement $r^2 \sim t^{3/2}$, reminiscent of some defects in experimental systems.

I will then show how non-reciprocal interactions imply that, on top of the topological charge, the actual shape of the defects becomes crucial to faithfully describe their dynamics. Non-reciprocal couplings twist the spin field, selecting specific defect shapes which in turn dramatically alters the BKT pair annihilation process. Depending on the shape of the defects and the degree of non-reciprocity in the system, the annihilation process can either be enhanced or hindered, featuring novel transverse forces as well as charge and shape dependent trajectories. Finally, I will show how this simple lattice model can provide intuition on and relation between the phenomenological coefficients of the Toner Tu equation.


References:
(A) Y. Rouzaire, D. Levis : https://arxiv.org/pdf/2103.12578 (PRL, 2021)
(A) Y. Rouzaire, D. Levis : https://www.frontiersin.org/articles/10.3389/fphy.2022.976515/full (Frontiers in Physics, 2022)
(B) Y. Rouzaire, D. Levis, I. Pagonabarraga, D. Pearce : https://arxiv.org/pdf/2401.12637 (arXiv, 4 pages, 2024)

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