Superconductivity Bridges Turbulence and Chirality, Demonstrating Emergent Inertial Regimes

Active matter, systems driven by internal forces, typically dissipates energy and exhibits disordered motion, yet recent work demonstrates that even these systems can surprisingly support turbulence resembling the smooth, persistent flows seen in fluids. Magnus F Ivarsen from University of Saskatchewan and colleagues now establish the underlying principles for this behaviour, revealing a fundamental connection between active turbulence and superconductivity. The researchers demonstrate a formal equivalence between the dynamics of self-propelled particles and the behaviour of disordered Josephson junctions, effectively identifying a collective state of these particles as a macroscopic superconducting phase. This discovery defines a new model for chiral flocking, framing it as a ‘motile Josephson array’ and offering a powerful new understanding of how complex, collective motion emerges from simple, dissipative interactions.

Active Matter Mimics Inertial Fluid Turbulence

The study establishes a connection between active matter and superconductivity by demonstrating that overdamped chiral active matter can exhibit emergent, inviscid Euler turbulence, despite its fundamentally dissipative nature. Researchers began by modeling the system as an ensemble of agents, each governed by a Langevin equation, and defined a continuum field theory to describe their collective behavior. This approach revealed a kinetic Turing instability, triggered by the interplay between activation and inhibition among the agents, mirroring observations in fluid dynamics. To address the emergence of inertial behavior in a dissipative system, the team considered the discrete distribution of agents as a spatially extended, disordered Josephson junction array, a concept borrowed from superconductivity.

This innovative approach allowed them to identify a depinning transition between ‘trapped’ and ‘running’ states, generating a macroscopic synchronization stiffness that effectively provides inertia to the system. The researchers drew a direct analogy to Josephson junctions, ensembles of quantum oscillators with inherent frequency variations, and leveraged the well-established Kuramoto model to provide a theoretical foundation for understanding the thermodynamics of their minimal model. To characterize the system’s behavior, the team derived an agent’s phase velocity in a co-moving frame, decomposing it into collective and relative components. This led to the definition of a phase slip velocity, quantifying an agent’s movement relative to the local potential well, and ultimately revealed a formal isomorphism with the Adler equation, a fundamental equation describing disordered Josephson arrays. The critical current, derived from the tilted washboard potential governing agent behavior, defines the threshold between trapped and running states, mirroring the transition between ordered and disordered phases in superconducting materials. This work demonstrates that the system bifurcates into a hydrodynamic, ordered state and an active, dissipative bath, offering a novel perspective on the interplay between active turbulence and superconductivity.

Active Matter Mirrors Superconducting Phase Transitions

Recent work demonstrates that overdamped, chiral active matter can exhibit emergent, inviscid Euler turbulence, despite its fundamentally dissipative nature. This research establishes the statistical mechanical foundation for this inertial regime by revealing a formal equivalence between the model’s agent dynamics and the overdamped Langevin equation governing disordered Josephson junctions. Scientists identified the trapped agent state as a macroscopic superconducting phase, described by the Adler equation, providing a crucial link between active matter and condensed matter physics. The validity of this mapping was analytically confirmed by observing a disorder-broadened Adler-Ohmic crossover in the system’s slip velocity, which corresponds to a saddle-node bifurcation in phase-locking systems.

Measurements of the slip velocity, defined as the absolute value of an agent’s phase velocity relative to the local potential well, pinpoint the transition between a hydrodynamic, ordered state and an active, disordered bath. This crossover demonstrates how the system bifurcates, establishing a clear connection between the microscopic agent behavior and macroscopic fluid dynamics. Researchers derived an agent’s phase velocity in a co-moving frame, decomposing it into collective and relative components, allowing for quantification of the slip velocity. This enabled the team to characterize the thermodynamics of the system, revealing a “shock cycle” between the active, dissipative bath and an ordered, inertial state. The results demonstrate that the system’s emergent inertia arises from a macroscopic synchronization stiffness generated by the transition between trapped and running states, effectively providing an inertial mass to the otherwise overdamped agents. This breakthrough delivers a novel understanding of how energy can cascade towards larger scales in a system that should fundamentally decay, bridging active turbulence and quantum superconductivity.

Chiral Flocks Mimic Superconducting Phase Behaviour

This research establishes a surprising connection between the behaviour of chiral active matter and the physics of superconductivity. Scientists have demonstrated that a minimalist model of overdamped chiral flocks exhibits emergent inertial turbulence, despite being fundamentally dissipative. Through rigorous mathematical analysis, they have identified a formal equivalence between the dynamics of these flocks and the behaviour of disordered Josephson junctions, key components in superconducting circuits. This mapping reveals that the system operates as a macroscopic superconducting phase, governed by the Adler equation, and exhibits a characteristic disorder-broadened Adler-Ohmic crossover in its slip velocity.

The team’s findings define the chiral flocking model as a motile, disordered Josephson array, effectively bridging the fields of active turbulence and superconductivity. This classification is supported by the system’s macroscopic response, which closely matches predictions derived from the resistively shunted junction formalism. The researchers acknowledge that the formal equivalence relies on the polar symmetry of the interactions within the flock, suggesting that different symmetries would lead to distinct behaviours. Future work explores the broader implications of this connection for understanding emergent spectral scaling and Onsager condensation in chiral active matter.

This work establishes phase synchronization as a fundamental mechanism driving macroscopic order, opening new avenues for exploring universality classes of driven chiral flocks. Active matter, systems driven by internal forces, typically dissipates energy and exhibits disordered motion, yet recent work demonstrates that even these systems can surprisingly support turbulence resembling the smooth, persistent flows seen in fluids. The researchers demonstrate a formal equivalence between the dynamics of self-propelled particles and the behaviour of disordered Josephson junctions, effectively identifying a collective state of these particles as a macroscopic superconducting phase.

This discovery defines a new model for chiral flocking, framing it as a ‘motile Josephson array’ and offering a powerful new understanding of how complex, collective motion emerges from simple, dissipative interactions. A formal isomorphism exists between the model’s agent dynamics and the overdamped Langevin equation for disordered Josephson junctions. The team identifies the trapped agent state as a macroscopic superconducting phase governed by the Adler equation. Analytical confirmation of this mapping comes from a disorder-broadened Adler-Ohmic crossover in the system’s slip velocity, which corresponds to the saddle-node bifurcation of phase-locking systems. These results define a new minimal chiral flocking model as a motile, disordered Josephson array, bridging active turbulence and quantum superconductivity.