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Fractional Floquet theory

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  • Iomin, Alexander

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.

Suggested Citation

  • Iomin, Alexander, 2023. "Fractional Floquet theory," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000978
    DOI: 10.1016/j.chaos.2023.113196
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    References listed on IDEAS

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    1. B. N. Narahari Achar & Bradley T. Yale & John W. Hanneken, 2013. "Time Fractional Schrodinger Equation Revisited," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-11, July.
    2. Iomin, Alexander, 2011. "Fractional-time Schrödinger equation: Fractional dynamics on a comb," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 348-352.
    3. Laskin, Nick, 2017. "Time fractional quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 16-28.
    4. Iomin, A., 2020. "Quantum dynamics and relaxation in comb turbulent diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Pierre Barthelemy & Jacopo Bertolotti & Diederik S. Wiersma, 2008. "A Lévy flight for light," Nature, Nature, vol. 453(7194), pages 495-498, May.
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    Cited by:

    1. Alexander Iomin, 2023. "Floquet Theory of Classical Relaxation in Time-Dependent Field," Mathematics, MDPI, vol. 11(13), pages 1-16, June.

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