Emergent Quantum Dynamics of Vortex Line under Linear Local Induction Approximation

TL;DR

This paper explores the quantum-like behavior of vortex lines under the linear local induction approximation, deriving an effective Schrödinger equation and path-integral formulation to better understand vortex dynamics and their analogy to quantum particles.

Contribution

It introduces a novel mapping between vortex line dynamics and quantum particle motion, deriving an effective Schrödinger equation and path-integral representation.

Findings

Derived the effective Schrödinger equation for vortex lines.

Established a path-integral formulation for vortex dynamics.

Proposed a vortex line-particle mapping to interpret quantum behavior.

Abstract

Using the linear local induction approximation, we investigated the self-induced motion of a vortex line that corresponds to the motion of a particle in quantum mechanics. Concerning Kelvin waves, the effective Schr\"odinger equation, physical quantities operators, and the corresponding path-integral formula are obtained. The vortex line-particle mapping may help in understanding particle motion in quantum mechanics.