Eur. Phys. J. B (2022) 95: 86
https://doi.org/10.1140/epjb/s10051-022-00337-6

Regular Article - A: Solid State and Materials

Breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain

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, Muizenberg, 7945, Cape Town, South Africa

^b djoufackzacharie@yahoo.fr, djoufack@aims.ac.za

Received: 13 December 2021
Accepted: 15 April 2022
Published online: 23 May 2022

Abstract

We study the breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain. By using the second quantification operators, we transform classical Hamiltonian into its quantum version, through Glauber’s coherent state representation in addition to the multiple-scale method, the 2D nonlinear Schrödinger equation (NLSE) is obtained. This NLSE is analytically solved by adopting the Rayleigh–Ritz variational method. Around impurity’s critical mass, we prove the existence of resonant structure. This critical mass is observed when plotting the frequency spectrum under the effect of the impurity mass and harmonic force constants. The effects of impurity mass and the harmonic force constants are found in the amplitude frequency spectra. When the breather interacts with the impurity, the system exhibit different scenario that are: barrier, well, excitation and chaotic all related to the trapping phenomenon. The modulational instability (MI) which helps to confirm the existence of breather is investigated. We have shown that impurity strength increases the instability regions, and the MI growth rate can be dramatically affected by the impurity mass around the critical value.