A Many-Body Extension to Madelung Quantum Hydrodynamics

ORAL

Abstract

In this talk we derive a many-body quantum-hydrodynamic model from first principles in the spirit of Madelung. We obtain exact time-dependent 3-D fluid equations that satisfy wave function symmetry or anti-symmetry, then obtain simplified forms for the cases of single permanent and Slater determinant with orthonormal basis functions. We show that, neglecting correlations and assuming many degenerate plane-wave electrons in the uniform limit, electron dynamics are governed by basic Euler equations with a mean-field Hartree interaction, Thomas–Fermi pressure, and Dirac exchange potential.

*The Flash Center acknowledges support by the U.S. DOE ARPA-E under Award DE-AR0001272, the NSF under Award PHY-2033925, and the U.S. DOE NNSA under Awards DE-NA0003842 and DE-NA0003856, and Subcontracts 536203 and 630138 with LANL and B632670 with LLNL. This work was performed under the auspices of the U.S. DOE by LLNL under Contract DE-AC52-07NA27344.

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Presenters

  • David Michta

    • University of Rochester

Authors

  • David Michta

    • University of Rochester

  • Frank R Graziani

    • Lawrence Livermore Natl Lab

  • Gregory W Hammett

    • Princeton Plasma Physics Laboratory
    • Princeton University

  • Petros Tzeferacos

    • University of Rochester