Quantum spin representation for the Navier-Stokes equation
Fluid Dynamics
2024-11-15 v2
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.
Cite
@article{arxiv.2403.00596,
title = {Quantum spin representation for the Navier-Stokes equation},
author = {Zhaoyuan Meng and Yue Yang},
journal= {arXiv preprint arXiv:2403.00596},
year = {2024}
}