On the Strong Coupling Techniques of Polaron Theory

P. Nagy

Ashok Chatterjee, Soma Mukhopadhyay

This chapter describes some of the most important theories of the strong-coupling polaron. The nature of polarons in the strong-coupling limit is in some sense qualitatively different from the weak or intermediate-coupling polaron—the localization of a polaron being a case in point. Though a qualitative picture of a strong-coupling polaron is easy to visualize as opposed to the weak-coupling polaron, the mathematical formulation of a strongly coupled polaron is rather a difficult problem from the quantum mechanical point of view. In fact, the exact polaron energy in the weak-coupling limit can be obtained from the Frohlich Hamiltonian analytically, while the same is not possible in the strong-coupling limit. In the strong-coupling case, the electron velocity is much larger than the phonon frequency and therefore electron can follow the ion motion adiabatically. The adiabatic expansion of the polaron energy in the strong-coupling regime was reported by Bogoliubov and Tiablikov.

Nikolay N. Bogolubov, Nikolay N. Bogolubov

Nikolay N. Bogolubov, Nikolay N. Bogolubov

J. T. Devreese, R. P. Evrard

Abstract The validity of Pekar's polaron theory is investigated by using it to solve Gross's simplified model in which the electron interacts with only one lattice oscillator. The results are compared with the exact solutions. This shows as expected, that Pekar's approximation provides an accurate strong coupling limit. The accuracy decreases with the mean number of virtual phonons, which is used to define the coupling strength. For a certain value of this parameter, Pekar's method becomes less accurate than the Lee‐Low‐Pines method. At this point the relative error is about 15%. The present study makes it possible to introduce an “intermediate coupling region” in Gross's model. In this region the relative error of the Lee‐Low‐Pines approximation is about 10%.