Interaction of hopfions of charge 1 and 2 from product ansatz

TL;DR

This paper investigates the interaction energy of axially symmetric Hopfions with charges 1 and 2 using a product ansatz, demonstrating its effectiveness at larger separations in both repulsive and attractive interactions.

Contribution

It extends the analysis of Hopfion interactions by applying the product ansatz to higher charge configurations and evaluates its validity across different separation regimes.

Findings

Product ansatz approximates Hopfion interactions well at larger separations.

Interaction patterns are consistent in both repulsive and attractive channels.

The approach provides insights into the behavior of higher-charge Hopfions.

Abstract

We continue the discussion on the interaction energy of the axially symmetric Hopfions evaluated directly from the product anzsatz. The Hopfions are given by the projection of Skyrme model solutions onto the coset space SU(2)/U(1). Our results show that if the separation between the constituents is not small, the product ansatz can be considered as a good approximation to the general pattern of Hopfions interaction both in repulsive and attractive channel.