A simple harmonic model as a caricature for mismatch and relaxation effects for ion hopping dynamics in solid electrolytes

摘要

We formulate a simple harmonic mean-field model with N +1 particles and analyze the relaxation processes following a jump of one of these particles. Either the particle can jump back (single-particle route) or the other N particles adjust themselves (multiparticle route). The dynamics of this model is solved analytically in the linear response regime. Furthermore, we relate these results to a phenomenological approach by Funke and co-workers (concept of mismatch and relaxtion, CMR) which has been successfully used to model conductivity spectra in the field of ion dynamics in solid electrolytes. Since the mean-field model contains the relevant ingredients of the CMR-approach, a comparison of the resulting rate equations with the CMR-equations becomes possible. Generalizations beyond the mean-field case are discussed.