PERIODIC-SOLUTIONS OF THE CLASSICAL POLARON AND BIPOLARON SYSTEMS

It is shown that the exact solutions for the classical polaron model derived by Evrard et al. (the electron rotates about a fixed polaron centre with frequency Ω≫ω) exist also for the discrete frequencies Ω = ω/(n+ 1/2)(ω is the longitudinal optical phonon frequency and n is an integer). For an infinite Brillouin zone radius the radius of the electron orbit is finite; this is in contrast with the behavior of the solutions found by Evrard et al., where the radius diverges with the Brillouin zone radius. Ringwood and Devreese have obtained the same set of solutions as proposed here with a different method. The present calculation shows clearly that the discrete frequencies arise as a consequence of the fact that the electron has to move in such a way that the different divergent contributions to the self-interaction cancel each other. For the bipolaron system similar exact solutions are found. It is shown that the orbit frequency of the electrons, in the bipolaron system, can have the values Ω = ω/(2n + 1). © 1980 American Institute of Physics.