Bloch Sphere Catastrophes

TL;DR

This paper explores caustic structures in spin-1/2 fields mapped onto the Bloch sphere, revealing stable topological defects and applying catastrophe theory to understand their formation and stability.

Contribution

It introduces a new type of stable topological defect in spin-1/2 fields and derives equations for their existence and unfolding based on catastrophe theory.

Findings

Caustic surfaces appear in spin-1/2 fields mapped to the Bloch sphere.

These structures are stable under perturbations.

The paper derives conditions for the existence and unfolding of these defects.

Abstract

Caustics are optical phenomena which occur when a family of rays creates an envelope of divergent intensity. Here we show that caustic surfaces also appear when a real or complex field is mapped to its order parameter manifold. We study these structures in the context of spin-1/2 fields, where the order parameter manifold is the Bloch sphere. These generic structures are a manifestation of catastrophe theory and are stable with respect to perturbations. The corresponding field configurations are also stable and represent a new type of topological defect. Equations governing the conditions for their existence and unfolding are derived.