Chaotic Zeeman effect: a fractional diffusion-like approch

• Published in: Scientific reports Vol. 14; no. 1; p. 6356
• Main Authors: Postavaru, Octavian, Stanescu, Mariana M.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 16-03-2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/624; 639/624/400; Atoms & subatomic particles; Calculus; Electrons; Energy; Humanities and Social Sciences; Magnetic fields; multidisciplinary; Science; Science (multidisciplinary)
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-024-57011-3

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