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Dynamical Manifestation of Chaotic Behaviour in a q-Tsallis Harmonic Oscillator

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Abstract

Recently, the q-deformed coherent states based on the non-extensive thermodynamics approach have been constructed (Chung et al. 2021; Jagannathan and Khan 2020; Bendjeffal et al. 2019). In this work, we analyse the dynamical behaviour of a quantum harmonic oscillator, which is initially prepared in this new formulation of q-coherent states. We investigate the signature of chaos by studying dynamics of expectation values of q-position and q-momentum operators. By examining the phase space diagrams, recurrence plots and the power spectrum of the time series, various dynamical regimes have been found. Our study shows that chaotic properties of the system, are related to the values of the Tsallis deformation parameter and the coherent amplitude. Finally, we have explicitly classified the chaotic nature of the system on the basis of these two parameters, the system is then found to be periodic, quasi-periodic or chaotic. As the value of the amplitude increases, the chaotic nature is the more prominent dynamical behaviour.

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Acknowledgements

I would like to express my thankfulness to Professor Leïla Ait-Gougam for her wonderful suggestions on the paper.

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  1. Theoretical Physics Laboratory (TPL), Faculty of Physics, University of Bab-Ezzouar, USTHB, B.P. 32, El Alia, Algiers, 16111, Algeria

    Radia Boudjema

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  1. Radia Boudjema
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Correspondence to Radia Boudjema.

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Boudjema, R. Dynamical Manifestation of Chaotic Behaviour in a q-Tsallis Harmonic Oscillator. Int J Theor Phys 61, 87 (2022). https://doi.org/10.1007/s10773-022-05073-2

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