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1 results

  • Holonomy and vortex structures in quantum hydrodynamics

  • Edited by Albert Fathi, Georgia Institute of Technology, Philip J. Morrison, University of Texas, Austin, Tere M-Seara, Universitat Politècnica de Catalunya, Barcelona, Sergei Tabachnikov, Pennsylvania State University
  • Book:
    Hamiltonian Systems
    Published online:
    10 May 2024
    Print publication:
    09 May 2024, pp 173-214

  • Summary

    We consider a new geometric approach to Madelung’s quantum hydrodynamics (QHD) based on the theory of gauge connections. Our treatment comprises a constant curvature thereby endowing QHD with intrinsic nonzero holonomy. In the hydrodynamic context, this leads to a fluid velocity which no longer is constrained to be irrotational and allows instead for vortex filaments solutions. After exploiting the Rasetti–Regge method to couple the Schrödinger equation to vortex filament dynamics, the latter is then considered as a source of geometric phase in the context of Born–Oppenheimer molecular dynamics. Similarly, we consider the Pauli equation for the motion of spin particles in electromagnetic fields and we exploit its underlying hydrodynamic picture to include vortex dynamics.