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The effect of time fractality on the transition coefficients: Historical Stern–Gerlach experiment revisited

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  • Şirin, Hüseyin
  • Büyükkılıç, Fevzi
  • Ertik, Hüseyin
  • Demirhan, Doğan

Abstract

In this article, the influence of time discreteness on the transition coefficients is investigated within the framework of time fractional development of quantum systems which has been developed recently by the present authors [22]. In this formalism, fractional mathematics which is a powerful tool to study the non-Markovian and non-Gaussian properties of physical processes is used in order to obtain time fractional evolution operator and transition probability. They are given in terms of Mittag–Leffler function which plays an important role in the mathematical structure as well as the physical interpretation of the phenomena under investigation. In order to place the presented formalism on a concrete basis, historical Stern–Gerlach experiment has been revisited with the purpose of studying transition coefficients which have a non-Markovian feature. The effect of the time fractionalization has been clearly illustrated in the figures via fractional derivative order α.

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  • Şirin, Hüseyin & Büyükkılıç, Fevzi & Ertik, Hüseyin & Demirhan, Doğan, 2011. "The effect of time fractality on the transition coefficients: Historical Stern–Gerlach experiment revisited," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 43-47.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:1:p:43-47
    DOI: 10.1016/j.chaos.2010.11.003
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    5. Şirin, H. & Büyükkılıç, F. & Ertik, H. & Demirhan, D., 2010. "The influence of fractality on the time evolution of the diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2007-2013.
    6. Ertik, H. & Demirhan, D. & Şirin, H. & Büyükkılıç, F., 2009. "A fractional mathematical approach to the distribution functions of quantum gases: Cosmic Microwave Background Radiation problem is revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4573-4585.
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    1. Wei, Dongmei & Liu, Hailing & Li, Yongmei & Gao, Fei & Qin, Sujuan & Wen, Qiaoyan, 2023. "Quantum speed limit for time-fractional open systems," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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