Noise-driven odd elastic waves in living chiral active matter

Abstract

Chiral active matter is predicted to exhibit odd elasticity, with nontraditional elastic response arising from a combination of chirality, being out of equilibrium, and the presence of nonreciprocal interactions. One of the resulting phenomena is the possible occurrence of odd elastic waves in overdamped systems, although its experimental realization still remains elusive. Here we show that in overdamped active systems, noise is required to generate persistent elastic waves. In the chiral crystalline phase of active matter, such as that found recently in populations of swimming starfish embryos, the noise arises from the self-driving of active particles and their mutual collisions, a key factor that has been missing in previous studies. We identify the criterion for the occurrence of noise-driven odd elastic waves and construct the corresponding phase diagram, which is also applicable to general chiral active crystals. Our results can be used to predict the experimental conditions for achieving a transition to self-sustained elastic waves in overdamped active systems.

Figures (4)

• Figure 1: (a) The dispersion results obtained from the current correlation function $C = C_{LL}+C_{TT}$ for the starfish embryo model in the presence of noise. The solid outer hexagon on the $(q_{x}, q_{y}$) plane at $\omega=0$ represents the reciprocal lattice, and the inner hexagon is the first Brillouin zone. (b) The dispersion relations along the red dashed line in the first Brillouin zone. Symbols correspond to the simulation results, while results obtained from the analytically calculated velocity correlation function are shown as solid or dashed curves. Large data variations around the $K$ point are due to the large uncertainties of data fitting for the near-zero noisy values of Re[$(1/N)\langle J_{L}^{*}J_{T} \rangle$] (see SM $\S$vii SM), which also leads to a big error bar showing as the vertical line in the middle of (b).
• Figure 2: Phase diagram of overdamped odd elastic systems as a function of noise strength $v_{\sigma}$ and the degree of nonreciprocity that is represented by the ratio $\alpha = k_{T}/k_{L}$. Induced by the noise, a new state of persistent noise-driven elastic waves appears at large enough $\alpha$ (regime iii). The purple star point denotes where the simulation for Fig. \ref{['fig:bandcomp']} is conducted, and the cyan cross point indicates the estimated location of the experimental starfish embryo system tan2022odd [with $\alpha$ calculated from experimental parameters and $v_{\sigma}$ deduced from the experimental data (SM $\S$xvi SM)]. Symbols of red circles and blue triangles represent results at the phase boundaries, as determined by simulations of the stochastic odd elastic model. The boundary at $\alpha_{0}=\sqrt{1/3}$ has been predicted by the deterministic theory scheibner2020odd. Sample cross sections of the phase diagram at $\alpha_{1}=0.79$ and $\alpha_{2}=2.63$ are provided in SM $\S$xi SM, showing transitions between different phases.
• Figure 3: The dispersion result obtained from the current correlation function $C$ for the starfish embryo experimental data of Ref. tan2022odd. (a) Data points with $C$ values exceeding a threshold of 0.075 are shown (to filter out noise), with the full plot given in SM $\S$xii SM. The outer and inner hexagons represent the reciprocal lattice and the first Brillouin zone respectively. Red dashed lines are added to indicate the location of the origin (red dot) and the frequency value $\omega = 0.03$ rad/s. Two signals per vertex are detected because the crystal changed its configuration during the experiment and thus slightly rotated in the co-rotating frame tan2022odd. (b) The top view of (a), where the coloring represents the maximum $C$ value at each $\mathbf{q}$. (c) Side view of (a) at $q_{x}=0$ (also corresponding to the red dashed line in (b)). (d) The dispersion result in the first Brillouin zone after removing the self-circling signal.
• Figure 4: (a) The dispersion results obtained from the current correlation function $C = C_{LL}+C_{TT}$ for the toy model in the presence of noise. The solid outer hexagon on the $(q_{x}, q_{y}$) plane at $\omega=0$ represents the reciprocal lattice, and the inner hexagon is the first Brillouin zone. (b) The dispersion relations along the red dashed line in the first Brillouin zone. Symbols correspond to the simulation results, while results obtained from the analytically calculated velocity correlation function are shown as solid or dashed curves. Large data variations around the $K$ point are due to the large uncertainties of data fitting for the near-zero noisy values of Re[$(1/N)\langle J_{L}^{*}J_{T} \rangle$] (see SM $\S$ vii SM).