Chaotic Zeeman effect: a fractional diffusion-like approch
Abstract 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 $$\theta $$ θ formed between the internal and the external magnetic field applied to the atom. The further...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-03-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-57011-3 |
| _version_ | 1797259293900144640 |
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| author | Octavian Postavaru Mariana M. Stanescu |
| author_facet | Octavian Postavaru Mariana M. Stanescu |
| author_sort | Octavian Postavaru |
| collection | DOAJ |
| description | Abstract 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 $$\theta $$ 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. |
| first_indexed | 2024-04-24T23:07:08Z |
| format | Article |
| id | doaj.art-8cf9188de8c04803830fd78825e483c4 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-24T23:07:08Z |
| publishDate | 2024-03-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-8cf9188de8c04803830fd78825e483c42024-03-17T12:24:13ZengNature PortfolioScientific Reports2045-23222024-03-011411710.1038/s41598-024-57011-3Chaotic Zeeman effect: a fractional diffusion-like approchOctavian Postavaru0Mariana M. Stanescu1Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of BucharestCenter for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of BucharestAbstract 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 $$\theta $$ 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.https://doi.org/10.1038/s41598-024-57011-3 |
| spellingShingle | Octavian Postavaru Mariana M. Stanescu Chaotic Zeeman effect: a fractional diffusion-like approch Scientific Reports |
| title | Chaotic Zeeman effect: a fractional diffusion-like approch |
| title_full | Chaotic Zeeman effect: a fractional diffusion-like approch |
| title_fullStr | Chaotic Zeeman effect: a fractional diffusion-like approch |
| title_full_unstemmed | Chaotic Zeeman effect: a fractional diffusion-like approch |
| title_short | Chaotic Zeeman effect: a fractional diffusion-like approch |
| title_sort | chaotic zeeman effect a fractional diffusion like approch |
| url | https://doi.org/10.1038/s41598-024-57011-3 |
| work_keys_str_mv | AT octavianpostavaru chaoticzeemaneffectafractionaldiffusionlikeapproch AT marianamstanescu chaoticzeemaneffectafractionaldiffusionlikeapproch |