量子流体动力学中的完整性与涡旋结构
Holonomy and vortex structures in quantum hydrodynamics
AI总结：
本文通过规范联络理论为量子流体动力学引入常曲率与内禀完整性，使流体速度可包含涡旋细丝解，并将涡旋动力学作为几何相来源纳入薛定谔方程和泡利方程。
摘要：
我们考虑一种基于规范联络理论的马德隆量子流体动力学（QHD）的新几何方法。特别地，我们的处理包含常曲率，从而赋予QHD内禀的非零完整性。在流体动力学语境下，这导致流体速度不再被约束为无旋，而是允许涡旋细丝解。在利用Rasetti-Regge方法将薛定谔方程与涡旋细丝动力学耦合之后，后者随后在Born-Oppenheimer分子动力学的语境中被视为几何相的来源。类似地，我们考虑自旋粒子在电磁场中运动的泡利方程，并利用其底层的流体动力学图像来纳入涡旋动力学。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
