论文标题
量子流体动力学中的载体和涡流结构
Holonomy and vortex structures in quantum hydrodynamics
论文作者
论文摘要
我们根据仪表连接理论考虑了Madelung量子流体动力学（QHD）的新几何方法。特别是，我们的处理包括一个恒定的曲率，从而使QHD具有固有的非零全体性。在流体动力的环境中，这导致流体速度不再被限制为无关，而是允许涡流丝解决方案。在利用rasetti-regge方法将schrödinger方程与涡流动力学息息后，后者被视为在Born-Oppenheimer分子动力学背景下的几何阶段的来源。同样，我们考虑了电磁场中自旋颗粒运动的Pauli方程，并利用其潜在的流体动力学图片来包括涡流动力学。
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.
