Chaotic Zeeman effect: a fractional diffusion-like approch

It is shown that the chaotic Zeeman effect of a quantum system can be formally viewed as a result of fractional calculus. The fractional calculation brings into the equations the angle \(\theta \) $\theta$ formed between the internal and the external magnetic field applied to the atom. The further the fractional coefficient \(\alpha \) $\alpha$ is from the ordinary case corresponding to \(\alpha =1\) $\alpha =1$ , the more important the chaotic effect is. The case corresponding to \(\alpha =1\) $\alpha =1$ does not depend on the angle \(\theta \) $\theta$ , obtaining the nonchaotic situation known in the literature. Non-Gaussian distributions correspond to non-stationary variables. Considering a Lorenzian type distribution, we can make a connection between the fractional formalism and random matrix theory. The connection validates the link between fractional calculus and chaos, and at the same time due to the \(\theta \) $\theta$ angle, it gives the phenomenon a physical interpretation.