Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics
We show, in the case of a special dipolar source, that electromagnetic fields in fractional quantum mechanics have an unexpected space dependence: propagating fields may have non-transverse components, and the distinction between near-field zone and wave zone is blurred. We employ an extension of Ma...
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| Format: | Article |
| Language: | English |
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Elsevier
2017-01-01
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| Series: | Results in Physics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S221137971630715X |
| _version_ | 1818948851686440960 |
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| author | Giovanni Modanese |
| author_facet | Giovanni Modanese |
| author_sort | Giovanni Modanese |
| collection | DOAJ |
| description | We show, in the case of a special dipolar source, that electromagnetic fields in fractional quantum mechanics have an unexpected space dependence: propagating fields may have non-transverse components, and the distinction between near-field zone and wave zone is blurred. We employ an extension of Maxwell theory, Aharonov-Bohm electrodynamics, which is compatible with currents jν conserved globally but not locally; we have derived in another work the field equation ∂μFμν=jν+iν, where iν is a non-local function of jν, called “secondary current”. Y. Wei has recently proved that the probability current in fractional quantum mechanics is in general not locally conserved. We compute this current for a Gaussian wave packet with fractional parameter a=3/2 and find that in a suitable limit it can be approximated by our simplified dipolar source. Currents which are not locally conserved may be present also in other quantum systems whose wave functions satisfy non-local equations. The combined electromagnetic effects of such sources and their secondary currents are very interesting both theoretically and for potential applications. Keywords: Generalized Maxwell theory, Fractional Schrödinger equation, Local current conservation |
| first_indexed | 2024-12-20T08:53:22Z |
| format | Article |
| id | doaj.art-a3f908713ec747779cd7f5f47df16397 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-20T08:53:22Z |
| publishDate | 2017-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-a3f908713ec747779cd7f5f47df163972022-12-21T19:46:04ZengElsevierResults in Physics2211-37972017-01-017480481Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamicsGiovanni Modanese0Free University of Bolzano-Bozen, P.za Universitá 5, Bolzano 39100, ItalyWe show, in the case of a special dipolar source, that electromagnetic fields in fractional quantum mechanics have an unexpected space dependence: propagating fields may have non-transverse components, and the distinction between near-field zone and wave zone is blurred. We employ an extension of Maxwell theory, Aharonov-Bohm electrodynamics, which is compatible with currents jν conserved globally but not locally; we have derived in another work the field equation ∂μFμν=jν+iν, where iν is a non-local function of jν, called “secondary current”. Y. Wei has recently proved that the probability current in fractional quantum mechanics is in general not locally conserved. We compute this current for a Gaussian wave packet with fractional parameter a=3/2 and find that in a suitable limit it can be approximated by our simplified dipolar source. Currents which are not locally conserved may be present also in other quantum systems whose wave functions satisfy non-local equations. The combined electromagnetic effects of such sources and their secondary currents are very interesting both theoretically and for potential applications. Keywords: Generalized Maxwell theory, Fractional Schrödinger equation, Local current conservationhttp://www.sciencedirect.com/science/article/pii/S221137971630715X |
| spellingShingle | Giovanni Modanese Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics Results in Physics |
| title | Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics |
| title_full | Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics |
| title_fullStr | Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics |
| title_full_unstemmed | Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics |
| title_short | Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics |
| title_sort | oscillating dipole with fractional quantum source in aharonov bohm electrodynamics |
| url | http://www.sciencedirect.com/science/article/pii/S221137971630715X |
| work_keys_str_mv | AT giovannimodanese oscillatingdipolewithfractionalquantumsourceinaharonovbohmelectrodynamics |