Information supercurrents and spin waves in chiral active matter: Universality of the Landau-Lifshitz-Gilbert equation

TL;DR

The paper addresses how overdamped polar chiral active matter can exhibit inertial, Euler-like turbulence. It develops a formal isomorphism to disordered Josephson junctions via an Adler-equation framework and a tilted washboard potential, revealing trapped versus running phases that transport phase information. Extending to three dimensions, it shows that Gilbert damping in a Landau-Lifshitz-Gilbert-like dynamics yields Goldstone spin waves (ferromagnetic magnons) that carry inertia for phase gradients, reconciling Toner-Tu second-sound concepts with spintronics. Together, these results provide a universal, lattice-free mechanism for information transport in active matter and propose a topological quasiparticle gas emerging from disorder-enabled phase rigidity.

Abstract

Recent minimalist modeling indicates that overdamped polar chiral active matter can support inviscid Euler turbulence, despite the system's strictly dissipative microscopic nature. In this article, we establish the statistical mechanical foundation for this emergent inertial regime by deriving a formal isomorphism between the model's agent dynamics and the overdamped Langevin equation for disordered Josephson junctions. We identify the trapped agent state as carrying non-dissipative phase rigidity supercurrents, a mapping we confirm empirically by demonstrating a disorder-broadened Adler-Ohmic crossover in the system's slip velocity. Generalizing this framework to three dimensions ($S^1\to S^2$), we show that polar alignment on the unit sphere is geometrically equivalent to the Gilbert damping term in spintronics, and that the two-dimensional Kuramoto coupling term naturally appears in the tangent-plane projection of spin relaxation. This constraint generates inertial spin waves (ferromagnetic magnons) from the overdamped active bath, recovering the macroscopic transport predicted by Toner-Tu theory without invoking microscopic inertia. Our results show that all polar chiral agents who seek to align on the unit sphere strictly constitute a dissipative spintronic fluid, where phase gradient transport is ensured by the Goldstone modes of the underlying broken symmetry.

Figures (6)

• Figure 1: A simulated ensemble of polar chiral active matter agents. Panels a--d) show end-state snapshots of the entire simulation space, with agent point-cloud (panel a), topological charge (panel b), flow-lines of circulation in order $R^2$(panel c), and agent slip velocity $v_\text{slip}$(panel d), with respective colorscales where applicable. In panel a), trapped agents are shown in black while running agents are shown in red.
• Figure 2: Panel a) shows defect count as a function of normalized simulation time (left $y$-axis) with a $t^{-0.75}$ powerlaw fit shown with a green, dashed line, and the average potential barrier height $\Delta(t)$ (Eq. \ref{['eq:barrier']}) in red (right $y$-axis, inverted). Panel b) shows a cross-correlation analysis of the latter two timeseries, for normalized times $>5$. Estimated confidence intervals for the cross-correlation are shown with dashed, black lines. Panels c--j) show inset $v_\text{slip}$ and trapped/running agent pointclouds, data from the black square in Figure \ref{['fig:art0']}d, in rapid succession-snapshots, highlighting ongoing shock merger, agent thermalization, and subsequent re-organization. See Video S1 in the Supplementary Materials for a video of this simulation run.
• Figure 3: The result of 256 simulations systematically varying the exponent in the $\omega_i$ distribution, yielding a systematically varied disorder strength $\Delta\omega$ (keeping the peak of the $\omega_i$ unchanged at $0.2$ s$^{-1}$, $\Delta\omega$ is calculated using the standard deviation), shown in the inset panel. The main plot shows observed ensemble average of the slip velocity $\langle v_\text{slip}\rangle$ (voltage) against dispersion $\Delta\omega$ (current), in a log-log "I-V" plot. $\langle v_\text{slip} \rangle$ is calculated as the mean value of $v_\text{slip}$ for all $N$ agents, collected during four snapshots of the second half of each simulation. A solid black line shows a $4^\text{th}$ order Hermite polynomial fit derrico_slm-shape_2009, while a dashed-blue line shows a $2^\text{nd}$ order (piece-wise linear) Hermite polynomial fit with slopes (exponent $\beta$) of 0 and 1. A vertical blue-dotted line indicates the theoretical mean-field critical threshold dispersion, $\Delta \omega_c \approx 6 \, \text{s}^{-1}$. The observable onset of slip velocity occurs significantly earlier (around $\Delta \omega \approx 0.5 \, \text{s}^{-1}$), indicating substantial sub-gap leakage current driven by the intrinsic disorder of the array.
• Figure 4: Panel a): the geometry of the 2D model, showing how the restoring force acts to align an agent's phase $\phi$ with the mean field $\Psi$. Panel b): the geometry of the 3D extension, where orientation is the unit vector on a spherical surface ($|\hat{\mathbf{n}}_i|=1$), and where the vector torque proportional to $(\hat{\mathbf{n}}_i \times \hat{\mathbf{\Psi}}) \times \hat{\mathbf{n}}_i$ (Eq. \ref{['eq:eom3d']}) acts to align the agent with the mean field, and represents spin relaxing to align with a magnetic field lakshmanan_fascinating_2011. This vector torque projects to the restoring force in panel a).
• Figure 5: The tilted washboard potential. Panel a): the $S^1$ potential wells $V(\theta)$ of the tilted washboard potential, traversed by phase mismatch $\theta$. Panel b): the $S^2$ potential wells, where potential energy $V(\theta)\propto -\cos\theta$ is independent of the azimuthal angle $\phi$, which means that the potential projects onto $S^1$ in mismatch $\theta$. This enables effortless precession around the mean field and directly activates the Goldstone mode dynamics (Eq. \ref{['eq:dispersion']}); a quasiparticle that advects phase gradients (turning stiffness), thereby mimicking inertial mass.