Quantum wave representation of dissipative fluids

Luca Salasnich, Sauro Succi and Adriano Tiribocchi
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Luca Salasnich: Dipartimento di Fisica e Astronomia “Galileo Galilei†and Padua QTech Center, Universitá di Padova — Via Marzolo, 8, Padova 35131, Italy2Sezione di Padova, INFN, — Via Marzolo, 8, Padova 35131, Italy3Istituto Nazionale di Ottica, CNR — Via Carrara, 1, Sesto Fiorentino 50019, Italy
Sauro Succi: Center for Life Nano Science@La Sapienza, Istituto Italiano, di Tecnologia 00161 Roma, Italy5Institute for Applied Computational Science, John A. Paulson, School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA6Istituto per le Applicazioni del Calcolo, CNR, Via dei Taurini 19, Rome 00185, Italy
Adriano Tiribocchi: Istituto per le Applicazioni del Calcolo, CNR, Via dei Taurini 19, Rome 00185, Italy7INFN “Tor Vergata†Via della Ricerca Scientifica 1, 00133 Roma, Italy

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 08, 1-10

Abstract: We present a mapping between a Schrödinger 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.

Keywords: Navier–Stokes equation; Schrödinger equation; Madelung equation; dissipation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124501006

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