Nonlinear response theory for Markov processes IV: The asymmetric double well potential model revisited

Abstract

The dielectric response of non-interacting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double well potential model does not follow the Langevin function and only in the linear regime the standard results are recovered. If a finite asymmetry is assumed, the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and the fifth-order response. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similar to the two-state model for high barriers. For small barriers no clearcut time scale separation between the barrier crossing process and the intra-well relaxation exists and the model exhibits a number of time scales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intra-well transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intra-well transitions play only role at the lowest temperatures.