The hydrodynamic representation of quantum mechanics describes virtual flow as if a quantum system were fluid in motion. This formulation illustrates pointlike vortices when the phase of a wavefunction becomes nonintegrable at nodal points. We study the dynamics of such pointlike vortices in the hydrodynamic representation for a two-particle wavefunction. In particular, we discuss how quantum entanglement influences vortex–vortex dynamics. For this purpose, we employ the time-dependent quantum variational principle combined with the Rayleigh–Ritz method. We analyze the vortex dynamics and establish connections with Dirac’s generalized Hamiltonian formalism.

中文翻译：

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量子力学流体动力学表示中纠缠对涡动力学的影响

量子力学的流体动力学表示描述了虚拟流动，就好像一个量子系统是运动的流体。当波函数的相位在节点处变得不可积时，该公式说明了点状涡旋。我们研究了双粒子波函数的流体动力学表示中这种点状涡旋的动力学。特别是，我们讨论了量子纠缠如何影响涡-涡动力学。为此，我们采用时间相关的量子变分原理与瑞利-里兹方法相结合。我们分析了涡流动力学并与狄拉克的广义哈密顿形式建立了联系。