Active Quantum Nematics: The First Quantization

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

Soft Condensed Matter (cond-mat.soft); Quantum Physics (quant-ph)

arXiv:2607.12961 [cond-mat.soft]

(or arXiv:2607.12961v2 [cond-mat.soft] for this version)

https://doi.org/10.48550/arXiv.2607.12961 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.