Fractional Floquet theory

Alexander Iomin

Chaos, Solitons & Fractals, 2023, vol. 168, issue C

Abstract: A fractional generalization of the Floquet theorem is suggested for fractional Schrödinger equations (FTSE)s with the time-dependent periodic Hamiltonians. The obtained result, called the fractional Floquet theorem (fFT), is formulated in the form of the Mittag-Leffler function, which is considered as the eigenfunction of the Caputo fractional derivative. The suggested formula makes it possible to reduce the FTSE to the standard quantum mechanics with the time-dependent Hamiltonian, where the standard Floquet theorem is valid. Two examples related to quantum resonances are considered as well to support the obtained result.

Keywords: Floquet theorem; Fractional Schrödinger equation; Caputo fractional derivative; Mittag-Leffler function (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000978

DOI: 10.1016/j.chaos.2023.113196

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