Topological influence and back-action between topological excitations

TL;DR

This paper develops a general theory of topological influence and back-action based on homotopy groups, revealing how topological objects interact and transfer charges, with applications to spin-2 Bose-Einstein condensates.

Contribution

It introduces a unified framework for topological influence and back-action using homotopy group commutators, and applies it to classify charge transfers in condensed matter.

Findings

Topological influence affects charge conservation in non-Abelian systems.

Back-action can restore total charge conservation through vortex twisting.

Non-Abelian charge transfer is demonstrated in spin-2 Bose-Einstein condensates.

Abstract

Topological objects can influence each other if the underlying homotopy groups are non-Abelian. Under such circumstances, the topological charge of each individual object is no longer a conserved quantity and can be transformed to each other. Yet, we can identify the conservation law by considering the back-action of topological influence. We develop a general theory of topological influence and back-action based on the commutators of the underlying homotopy groups. We illustrate the case of the topological influence of a half-quantum vortex on the sign change of a point defect and point out that the topological back-action from the point defect is such twisting of the vortex that the total twist of the vortex line carries the change in the point-defect charge to conserve the total charge. We use this theory to classify charge transfers in condensed matter systems and show that a non-Abelian charge transfer can be realized in a spin-2 Bose-Einstein condensate.