ABSTRACT
The effect of the dimensionality in general on the properties of a large optical polaron has been first studied by Peeters et al. by generalizing the Frohlich Hamiltonian to N dimensions. The basic idea is to obtain the Frohlich Hamiltonian of a lower-dimensional system from that of a higher one by integrating out the extra dimensions. The scaling analysis of the adiabatic eigenstates of a carrier placed in a deformable continuous medium by Emin and Holstein shows how the nature of an adiabatic polaron depends on the range and strength of the electron-lattice interaction and on the dimensionality of the system. The extension of the Landau-Pekar method to the N-dimensional bound polaron problem from the corresponding free-polaron case is straight-forward. Comparison of the Feynman-Haken path-integral results with the Lee-Low-Pines-Huybrechts (LLPH) results shows that the Feynman-Haken results are always lower than LLPH results except for the localized state hydrogenic approximation when the two theories give the same results.
