Effect of different site energies on polaronic properties

Using the perturbation method based on a variational phonon basis obtained by the modified Lang-Firsov (MLF) transformation, the two-site single polaron Holstein model is studied in presence of a difference in bare site energies ($\epsilon_d$=$\epsilon_2$-$\epsilon_1$). The polaronic ground-state wave function is calculated up to the fifth order of perturbation. The effect of $\epsilon_d$ (acts as a site-energy disorder) on the polaron crossover, polaronic kinetic energy, oscillator wavefuncion and polaron localization are studied. Considering a double-exchange Holstein model with finite $\epsilon_d$, role of disorder on the properties of the double-exchange system is also discussed.