Microscopic Hamiltonian and chaotic behavior for Barium Titanate nanoparticles revealed by photonic tunneling model

Abstract

In order to understand the microscopic properties of the ferroelectric nanoparticles, we review concepts of the attractive BaTiO3 crystals where a photon field from its constituent electrons and ions are considered. We present an associated Hamiltonian and extended potential which are the bases of the physical description of the system from certain geometry of the semiquantal space with the specific phonon mode. Furthermore, we formulate the nonlinear dynamics equation of the systems with the famous microscopic Hamiltonian and Heisenberg equation of motion. In addition, we interest ourselves to a system of BaTiO3 crystals and hypothesis leading to order-disorder nature of phase transitions. The latter are linked to the cooperative phenomenon of chains. The numerical simulations reveal that complex behaviors propagate in such system that can be useful for future application of Barium Titanate crystals in modern electronic technologies.