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arXiv · 2403.00596

Quantum spin representation for the Navier-Stokes equation

Zhaoyuan Meng·Yue Yang
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Abstract

We develop a quantum representation for Newtonian viscous fluid flows by establishing a mapping between the Navier-Stokes equation (NSE) and the Schr\"odinger-Pauli equation (SPE). The proposed nonlinear SPE incorporates the two-component wave function and the imaginary diffusion. Consequently, classical fluid flow can be interpreted as a non-Hermitian quantum spin system. Using the SPE-based numerical simulation of viscous flows, we demonstrate the quantum/wave-like behavior in flow dynamics. Furthermore, the SPE equivalent to the NSE can facilitate the quantum simulation of fluid dynamics.

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Zhaoyuan Meng, Yue Yang. 2024-03-01. Quantum spin representation for the Navier-Stokes equation. https://doi.org/10.1103/physrevresearch.6.043130

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