Simon Böhly, From quantum mechanics to classical fluid dynamics: the Schrödinger-Navier-Stokes equation

by Simon Böhly (Erasmus scholar from Heidelberg)

Wednesday 22 Jul 2026, 11:00 → 12:00 Europe/Rome

1/3-1 - Sala R (Dipartimento di Fisica e Astronomia - Edificio Marzolo)

The Madelung transformation was introduced in 1927 by Erwin Madelung and showed that the Schrödinger equation can be cast into a form reminiscent of classical fluid dynamics.This analogy becomes even richer for quantum systems governed by a so-called nonlinear Schrödinger equations, such as Bose–Einstein condensates described by the Gross-Pitaevskii equation, where phenomena including superfluidity and quantized vortices emerge naturally. Motivated by these connections, recent work has revisited the relationship between nonlinear quantum wave equations and the classical Navier–Stokes equation. In this talk, we present the motivation and main results of two recent papers [1,2] showing that a suitably modified nonlinear Schrödinger equation provides a wave representation of the irrotational viscous Navier–Stokes equations, and discuss its extension to capillary fluids. Finally, we outline ongoing work aimed at incorporating vorticity into this framework through the introduction of a U(1) gauge field, with the goal of extending the formalism to rotational viscous flows.

[1] L. Salasnich, S. Succi, and A. Tiribocchi, Quantum wave representation of dissipative fluids, Int. J. Mod. Phys. C 35, 2450100 (2024).

[2] L. Salasnich, S. Böhly, S. Succi, and A. Tiribocchi, Schrödinger-Navier-Stokes equation for capillary fluids, Phys. Fluids 38, 078110 (2026).