Holonomy and vortex structures in quantum hydrodynamics
| Autor: | Foskett, Michael S., Tronci, Cesare |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | In "Hamiltonian Systems: Dynamics, Analysis, Applications". Edited by A. Fathi, P. J. Morrison, T. M-Seara, and S. Tabachnikov. Math. Sci. Res. Inst. Pub. 72. Pages 173-214. Cambridge University Press. 2024 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/9781009320733.006 |
| Popis: | 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 Schr\"odinger 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. Comment: 34 pages, no figures. To appear in Math. Sci. Res. Inst. Publ |
| Databáze: | arXiv |
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