An analogous Wu-Yang monopole in superfluid

TL;DR

This paper demonstrates an analogy between Wu-Yang monopoles and superfluid ${^3}$He by linking hydrodynamic equations to quantum mechanics, revealing new insights into monopole simulation within superfluid systems.

Contribution

It introduces an effective potential in the Schrödinger equation derived from superfluid hydrodynamics, establishing an analogy with Wu-Yang monopoles and exploring their physical implications.

Findings

Identification of hydrodynamic solutions as Wu-Yang monopole analogs

Role of the constraint $ abla ho ext{·} extbf{v}=0$ in monopole harmonic selection

Potential for simulating Wu-Yang monopoles using superfluid ${^3}$He

Abstract

By identifying the Schr\"{o}dinger equation with the hydrodynamic equations in superfluid ${^3}$He, the effective potential is introduced in the Schr\"{o}dinger equation to solve the quantum pressure in steady state. The pure gauge velocity solutions of hydrodynamic equations provide an analogous Wu-Yang monopole potential. The two cases of velocity in superfluid are equivalent to the two regions of Wu-Yang monopole potential. Due to the compressibility of superfluid, the physical models are limited, such as hard core and harmonic oscillator. It is important that the constraint condition of $\nabla\rho\cdot \textbf{v}=0$ plays a key role, which determines that the integral quantum numbers are selected in monopole harmonics and shows the special analogous Wu-Yang monopole. The results provide a new possibility for the simulation of Wu-Yang monopole.