This qualitatively explains the widespread occurrence of long-range behavior in chaotic dynamics known as [[pink noise|1/f noise]].<ref name =":10"></ref> A more rigorous theoretical explanation of 1/f noise remains an open problem.
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=== Pseudo-time reversal symmetry breaking ===
When <math>H_g</math> is complex, [[#Eigensystem of GTO|pseudo-time-reversal symmetry]] is also spontaneously broken. In the context of [[Dynamo theory#Kinematic dynamo theory|kinematic dynamo]], this situation corresponds to rotation of the galactic magnetic field.<ref name=":22">{{Cite journal|last1=Ovchinnikov|first1=I.V.|last2=Ensslin|first2=T. A.|date=2016|title=Kinematic dynamo, supersymmetry breaking, and chaos|journal=Physical Review D|volume=93|issue=8|pages=085023|doi=10.1103/PhysRevD.93.085023|bibcode=2016PhRvD..93h5023O|arxiv=1512.01651|s2cid=59367815}}</ref> The implications of complex <math>H_g</math> in a more general setting remain unexplored.
