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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.06489 |
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| _version_ | 1866910906962673664 |
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| author | Molina, Mario I. |
| author_facet | Molina, Mario I. |
| contents | We examine the effect of fractionality on the bloch oscillations (BO) of a 1D tight-binding lattice when the discrete Laplacian is replaced by its fractional form. We obtain the eigenmodes and the dynamic propagation of an initially localized excitation in closed form as a function of the fractional exponent and the strength of the external potential. We find an oscillation period equal to that of the non-fractional case. The participation ratio is computed in closed form and it reveals that localization of the modes increases with a deviation from the standard case, and with an increase of the external constant field. When nonlinear effects are included, a competition between the tendency to Bloch oscillate, and the trapping tendency typical of the Kerr effect is observed, which ultimately obliterates the BO in the limit of large nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Bloch oscillations Molina, Mario I. Pattern Formation and Solitons We examine the effect of fractionality on the bloch oscillations (BO) of a 1D tight-binding lattice when the discrete Laplacian is replaced by its fractional form. We obtain the eigenmodes and the dynamic propagation of an initially localized excitation in closed form as a function of the fractional exponent and the strength of the external potential. We find an oscillation period equal to that of the non-fractional case. The participation ratio is computed in closed form and it reveals that localization of the modes increases with a deviation from the standard case, and with an increase of the external constant field. When nonlinear effects are included, a competition between the tendency to Bloch oscillate, and the trapping tendency typical of the Kerr effect is observed, which ultimately obliterates the BO in the limit of large nonlinearity. |
| title | Fractional Bloch oscillations |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2504.06489 |