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arXiv · 2308.05879

Quantum wave representation of dissipative fluids

L. Salasnich·S. Succi·A. Tiribocchi
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Abstract

We present a mapping between a Schr\"odinger equation with a shifted non-linear potential and the Navier-Stokes equation. Following a generalization of the Madelung transformations, we show that the inclusion of the Bohm quantum potential plus the laplacian of the phase field in the non-linear term leads to continuity and momentum equations for a dissipative incompressible Navier-Stokes fluid. An alternative solution, built using a complex quantum diffusion, is also discussed. The present models may capture dissipative effects in quantum fluids, such as Bose-Einstein condensates, as well as facilitate the formulation of quantum algorithms for classical dissipative fluids.

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L. Salasnich, S. Succi, A. Tiribocchi. 2023-08-10. Quantum wave representation of dissipative fluids. https://doi.org/10.1142/s0129183124501006

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