Chaotic Zeeman effect: a fractional diffusion-like approch

Abstract

AbstractIt 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 $$\theta $$ θ formed between the internal and the external magnetic field applied to the atom. The further the fractional coefficient $$\alpha $$ α is from the ordinary case corresponding to $$\alpha =1$$ α = 1 , the more important the chaotic effect is. The case corresponding to $$\alpha =1$$ α = 1 does not depend on the angle $$\theta $$ θ , 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 $$\theta $$ θ angle, it gives the phenomenon a physical interpretation.