Active Quantum Nematics: The First Quantization

This paper explores the mathematical parallels between active nematics—systems of self-propelled particles like bacteria or synthetic micro-swimmers—and quantum mechanics. The authors seek to bridge the gap between continuum hydrodynamics and quantum theory by introducing a complex-valued nematic wavefunction, denoted as ψ, into the standard Beris-Edwards equations. By treating the nematic system as a collection of quantized states, the authors aim to provide a unified framework for describing the spatiotemporal evolution of active matter, ranging from bacterial colonies to the contractile activity of heart tissue.

By incorporating a complex phase-symmetry into the governing equations, the authors derive a Planck-like energy-frequency relationship (E = ℏAω) for active micro-swimmers, where ℏA acts as an active nematic Planck constant. This formulation allows the researchers to treat active matter as a system of superimposed eigenstates within a Hilbert space.

Key results include:

• Peristaltic Motion: The framework successfully recovers the 'Scallop theorem' for reciprocating swimmers, showing that net motion requires a spatial gradient in the complex phase (breaking time-reversal symmetry).
• Chemotaxis: The model provides a description of predator-prey dynamics, where organisms evolve to maximize or minimize pheromone field gradient overlaps.
• Biological Characterization: The state-function approach allows for the characterization of beating hearts beyond simple rhythm, capturing the spatiotemporal distribution of contractile harmonics, which could potentially distinguish between healthy and unhealthy states.

This work provides a novel theoretical lens for active matter, suggesting that complex-valued wavefunctions can effectively model the collective behavior of biological and synthetic active systems. By mapping fluid-dynamical systems onto a quantum-like structure, the authors offer a new set of tools—such as uncertainty principles and eigenvalue analysis—to analyze complex, non-equilibrium systems that are otherwise difficult to track using standard statistical mechanics.