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 formed between the internal and the external magnetic field applied to the atom. The further the fractional coefficient is from the ordinary case corresponding to , the more important the chaotic effect is. The case corresponding to does not depend on the angle , 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 angle, it gives the phenomenon a physical interpretation.