Order and chaos in the SU(2) matrix model: Ergodicity and classical phases

We study the classical nonlinear dynamics of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo></a:math> Yang-Mills matrix model introduced in [] as a low-energy approximation to two-color QCD. Restricting to the spin-0 sector of the model, we unearth an unexpected tetrahedral symmetry, which endows the dynamics with an extraordinarily rich structure. Among other things, we find that the spin-0 sector contains coexisting chaotic subsectors as well as nested chaotic “basins”, and displays alternation between regular and chaotic dynamics as energy is varied. The symmetries also grant us a considerable amount of analytic control which allows us to make several quantitative observations. We see that the classical spin-0 sector has a rich phase structure, arising from ergodicity breaking. Surprisingly, we find that many of these classical phases display numerous similarities to previously discovered phases of the spin-0 sector [], and we explore these similarities in a heuristic fashion. Published by the American Physical Society 2024