https://doi.org/10.1140/epjp/s13360-024-04973-y
Review
Scattering of impure mode and self-trapping phenomenon in a 1D quantum diatomic Klein–Gordon chain containing a mass defect
1
Pure Physics Laboratory: Group of Nonlinear Physics and Complex Systems, Department of Physics, University of Douala, P.O. Box, 24157, Douala, Cameroon
2
Unité de Recherche d’Automatique et Informatique Apliquée (UR-AIA), Fotso Victor University Institute of Technology, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
3
The African Institute for Mathematical Sciences (AIMS), 6 Melrose Road, 7945, Muizenberg, Cape Town, South Africa
b djoufackzacharie@yahoo.fr, isidore.djoufack@univ-dschang.org
Received:
4
December
2023
Accepted:
4
February
2024
Published online:
26
February
2024
We analyze the impurity effects on the existence of localized structures, modulational instability (MI) and energy localization in a 1D quantum diatomic Klein–Gordon chain containing a mass defect. We have found that the impurities significantly affect the vibrational properties of crystals by modifying the distribution of normal mode frequencies. The MI investigation shows that, on the one hand, the mass defect around its critical value can dramatically influence the instability areas and the growth rate; on the other hand, the system exhibits an intrinsic asymmetry property that influences the localization and propagation of the impure mode. The conditions of stability of the impure mode are presented and a scattering phenomenon is observed when the impure mode is unstable. This phonons scattering phenomenon can be controlled either by the mass impurity , by the coupling term c and by the pure mass
. The accuracy of the analytical analysis has been performed by the numerical simulations and an excellent agreement has been observed. Furthermore, we have found through the energy localization that the impure mode can develop a local accumulation of energy known as self-trapping phenomenon.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.