Chaos in QCD? Gap Equations and Their Fractal Properties

Abstract

In this study, we discuss how iterative solutions of QCD-inspired gap-equations at the finite chemical potential demonstrate domains of chaotic behavior as well as non-chaotic domains, which represent one or the other of the only two—usually distinct—positive mass gap solutions with broken or restored chiral symmetry, respectively. In the iterative approach, gap solutions exist which exhibit restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally broken, non-chaotic domain with no emergent mass poles and hence with no quasi-particle excitations exists below this energy cut-off. The transition domain between these two energy-separated domains is chaotic. As a result, the dispersion relation is that of quarks with restored chiral symmetry, cut at a dynamical energy scale, and determined by fractal structures. We argue that the chaotic origin of the infrared cut-off could hint at a chaotic nature of confinement and the deconfinement phase transition.