Fractional Bloch oscillations

Mario I. Molina

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arXiv · 2504.06489

Fractional Bloch oscillations

Mario I. Molina

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Abstract

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.

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Mario I. Molina. 2025-04-08. Fractional Bloch oscillations. https://arxiv.org/abs/2504.06489

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