Quantum wave representation of dissipative fluids

• Main Authors: Salasnich, L, Succi, S, Tiribocchi, A
• Format: Journal Article
• Language: English
• Published: 02-01-2024
• Subjects: Physics - Fluid Dynamics; Physics - Quantum Physics
• DOI: 10.48550/arxiv.2308.05879

International Journal of Modern Physics C, Vol. 35, No. 08,
2450100 (2024) 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.