Energy Bounds of Linked Vortex States

TL;DR

This paper investigates the energy bounds of knotted and linked vortex states in a charged two-component system, revealing new universal classes and energy conditions related to linking numbers and the Hopf invariant.

Contribution

It introduces new classes of universal vortex states and establishes energy bounds based on linking numbers and the Hopf invariant in charged two-component systems.

Findings

Linked vortex states have lower energy when mutual linking number is less than the Hopf invariant.

New classes of universal vortex states are identified as local minima of free energy.

Energy bounds depend on topological linking properties of vortex lines.

Abstract

Energy bounds of knotted and linked vortex states in a charged two-component system are considered. It is shown that a set of local minima of free energy contains new classes of universality. When the mutual linking number of vector order parameter vortex lines is less than the Hopf invariant, these states have lower-lying energies.