Quantum wave representation of dissipative fluids

• URL: http://arxiv.org/abs/2308.05879v2
• Date: Tue, 2 Jan 2024 20:36:10 GMT
• Title: Quantum wave representation of dissipative fluids
• Abstract summary: We present a mapping between a Schr"odinger equation with a shifted non-linear potential and the Navier-Stokes equation. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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