Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect
We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Usi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2021-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/abe445 |
| _version_ | 1827872754526846976 |
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| author | J Bělín T Tyc S A R Horsley |
| author_facet | J Bělín T Tyc S A R Horsley |
| author_sort | J Bělín |
| collection | DOAJ |
| description | We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds. |
| first_indexed | 2024-03-12T16:28:20Z |
| format | Article |
| id | doaj.art-500ebebc8dfb457aa080af50c43deafa |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:28:20Z |
| publishDate | 2021-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-500ebebc8dfb457aa080af50c43deafa2023-08-08T15:35:28ZengIOP PublishingNew Journal of Physics1367-26302021-01-0123303300310.1088/1367-2630/abe445Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effectJ Bělín0https://orcid.org/0000-0002-8801-1606T Tyc1https://orcid.org/0000-0002-7565-6958S A R Horsley2School of Physics and Astronomy, College of Science and Engineering, University of Glasgow , Glasgow G12 8QQ, United Kingdom; Central European Institute of Technology, Brno University of Technology , Purkyňova 656/123, 612 00 Brno, Czech RepublicDepartment of Theoretical Physics and Astrophysics, Faculty of Science , Masaryk University, Kotlářská 2, 61137 Brno, Czech RepublicDepartment of Physics and Astronomy, Stocker Road, University of Exeter , Exeter EX4 4QL, United KingdomWe analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.https://doi.org/10.1088/1367-2630/abe445curved spacesquantum revivalsTalbot effecttopologyorbifolds |
| spellingShingle | J Bělín T Tyc S A R Horsley Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect New Journal of Physics curved spaces quantum revivals Talbot effect topology orbifolds |
| title | Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect |
| title_full | Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect |
| title_fullStr | Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect |
| title_full_unstemmed | Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect |
| title_short | Optical simulation of quantum mechanics on the Möbius strip, Klein’s bottle and other manifolds, and Talbot effect |
| title_sort | optical simulation of quantum mechanics on the mobius strip klein s bottle and other manifolds and talbot effect |
| topic | curved spaces quantum revivals Talbot effect topology orbifolds |
| url | https://doi.org/10.1088/1367-2630/abe445 |
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