Quantum wave representation of dissipative fluids

Year: 2024

Authors: Salasnich L., Succi S., Tiribocchi A.

Autors Affiliation: Univ Padua, Dipartimento Fis & Astron Galileo Galilei, Via Marzolo 8, I-35131 Padua, Italy; Univ Padua, Padua QTech Ctr, Via Marzolo 8, I-35131 Padua, Italy; INFN, Sez Padova, Via Marzolo 8, I-35131 Padua, Italy; CNR, Ist Nazl Ott, Via Carrara 1, I-50019 Sesto Fiorentino, Italy; Ist Italiano Tecnol, Ctr Life Nano Sci La Sapienza, I-00161 Rome, Italy; Harvard Univ, Inst Appl Computat Sci, John A Paulson Sch Engn & Appl Sci, Cambridge, MA 02138 USA; CNR, Ist Applicaz Calcolo, Via Taurini 19, I-00185 Rome, Italy; INFN Tor Vergata, Via Ric Sci 1, I-00133 Rome, Italy.

Abstract: We present a mapping between a Schrodinger equation with a shifted nonlinear 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 nonlinear 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.

Journal/Review: INTERNATIONAL JOURNAL OF MODERN PHYSICS C

Volume: 35 (8)      Pages from:   to:

More Information: S. Succi acknowledges illuminating discussions with Prof. Michael Berry. He also acknowledges financial support from the Flatiron Institute at the Simons Foundation, where part of this work was performed. L. Salasnich is partially supported by the European Quantum Flagship Project PASQuanS 2, by the European Union-NextGenerationEU within the National Center for HPC, Big Data and Quantum Computing [Project No. CN00000013, CN1 Spoke 10: QuantumComputing], by the BIRD Project Ultracold atoms in curved geometries of the University of Padova, by Iniziativa Specica Quantum of INFN, and by PRIN Project Quantum Atomic Mixtures: Droplets, Topological Structures andVortices of the Italian Ministry for Universities and Research.
KeyWords: Navier-Stokes equation; Schrodinger equation; Madelung equation; dissipation
DOI: 10.1142/S0129183124501006

Citations: 2
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