# Effects of entanglement on vortex dynamics in the hydrodynamic representation of quantum mechanics

## TL;DR

This paper investigates how quantum entanglement affects vortex dynamics within the hydrodynamic framework of quantum mechanics, revealing the influence of entanglement on vortex interactions and motion.

## Contribution

It introduces a detailed analysis of entanglement's role in vortex dynamics using variational principles and Hamiltonian formalism in the hydrodynamic representation.

## Key findings

- Entanglement significantly alters vortex-vortex interactions.
- Vortex dynamics are connected to Dirac's Hamiltonian formalism.
- The study provides a new perspective on quantum fluid behavior.

## Abstract

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.