Active Quantum Nematics: The First Quantization
arXiv:2607.12961
The paper introduces a complex-valued nematic wavefunction to recast active nematic and liquid crystal dynamics in a quantum‑mechanical framework, yielding quantized states and analogues of Planck’s energy‑frequency relation for microswimmers and biological rhythms.
Abstract
Nematic symmetry entails conserved quantized quantities such as number of topological defects and vorticity cells. Correspondingly, countless quantum analogies have been found in Active Nematics. We formalize Active Nematics and Liquid Crystal theory into the framework of Quantum Mechanics by introducing a complex valued Nematic Wavefunction to the Beris Edward equations, thus splitting spatiotemporally varying nematic systems into quantized states. We obtain the Planck's energy-frequency relationship for active micro-swimmers such as peristaltic worms and bacterium as a consequence of local complex phase-symmetry of the governing equations, similar to the gauge formulation of Electromagnetism. For organisms operating on diffusive chemotaxis, we obtain predator-prey dynamics that evolve to maximize/minimize pheromones field gradient overlap. Furthermore, when quantizing beating hearts, similar to the orbitals of hydrogen atoms, the state-function allows us to characterize hearts not only through the rhythm, but also the spaciotemporal distribution of contractile activity of various harmonics among healthy and unhealthy hearts.
21 Pages, Double Spaced, 4 figures. Towards PhD thesis work of Ghansham Chandel, under the guidance of Dr Siddhartha Das