2020/03/19 by Foskett, Michael S., Tronci, Cesare · 1 citation
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2003.08664
We consider a new geometric approach to Madelung's quantum hydrodynamics (QHD) based on the theory of gauge connections. In particular, our treatment comprises a constant curvature thereby endowing QHD with intrinsic non-zero 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.