Bloch Sphere Catastrophes
Optics
2014-06-05 v1 Statistical Mechanics
Mathematical Physics
math.MP
Quantum Physics
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.
Cite
@article{arxiv.1406.0583,
title = {Bloch Sphere Catastrophes},
author = {Samuel A. Eastwood and David M. Paganin and Timothy C. Petersen and Michael J. Morgan},
journal= {arXiv preprint arXiv:1406.0583},
year = {2014}
}