Kinetics of Nb incorporation into barium titanate

Influences of the non-adiabatic phonon fluctuations on the ground state, and on the minimum uncertainty principle of phonons were investigated by introducing a new state-ansatz including correlation between the displacement and squeezing of the phonons in the strongly coupled electron-phonon systems. For a large squeezing, the correlation lowers, obviously, the energy of the ground state, and increases the binding energy of the polaron when compared with the uncorrelated case. Thus the stabilization of the polarons and the stability of the systems are all enhanced. The correlation was also found to suppress the quantum reduction of the classical narrowing of the polaron band, and to weaken the tunnelling effect of the polarons, and to enhance the quantum uncertainty for the phonon coordinate due to the coupling with the electron density fluctuation. Generally, the correlated effects and new ansatz introduced here were found to be relevant for a sufficiently large squeezing in the strongly and intermediately coupled electron-phonon systems.