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  • Open Access

Quantum corrections at second order in derivatives to the dynamics of small nonrelativistic fluids

Lars H. Heyen*

Giuliano Giacalone†

Stefan Floerchinger‡

  • Scientific Computing Center, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany and Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

  • Theoretical Physics Department, CERN, CH-1211 Genève 23, Switzerland and Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

  • *Contact author: lars.heyen@kit.edu
  • †Contact author: giuliano.giacalone@cern.ch
  • ‡Contact author: stefan.floerchinger@uni-jena.de
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Phys. Rev. C 112, 014003 – Published 8 July, 2025

DOI: https://doi.org/10.1103/fx1y-37hq

Abstract

To capture the dynamics of macroscopic nonrelativistic fluids consisting of very many atoms, it is typically sufficient to truncate the gradient expansion at order zero, leading to ideal fluid dynamics, or at order one, leading to the Navier-Stokes theory. For mesoscopic fluids consisting of a small number of atoms, second-order corrections can become significant. We investigate here specifically superfluids at vanishing temperature and identify relevant second-order terms of quantum origin that contribute already in a static situation. The general form of these terms arises from an extension of the Gross-Pitaevskii theory. In the context of density functional theory, they are named after C. von Weizsäcker. We assess the influence of these terms on numerical solutions of second-order fluid dynamic equations for the expansion of a mesoscopic ultracold Fermi gas released from an anisotropic harmonic trap in two spatial dimensions.

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Phys. Rev. C 112, 014003– Published 8 July, 2025
  • Received 20 September 2024
  • Accepted 30 May 2025
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