Nonlinear response theory for Markov processes III: Stochastic models for dipole reorientations

Abstract: The nonlinear response of molecular systems undergoing Markovian stochastic reorientations is calculated up to fifth order in the amplitude of the external field. Time-dependent perturbation theory is used to compute the relevant response functions as in earlier treatments (G. Diezemann, Phys. Rev. E{\bf 85}, 051502 (2012), Phys. Rev. E{\bf 96}, 022150 (2017)). Here, we consider the reorientational motion of isolated molecules and extend the existing calculations for the model of isotropic rotational diffusion to the model of anisotropic rotational diffusion and to the model of rotational random jumps. Depending on the values of some model parameters, we observe a hump in the modulus of the nonlinear susceptibility for either of these models. Interestingly, for the model of rotational random jumps, the appearance of this hump depends on the way the coupling to the external field is modelled in the master equation approach. If the model of anisotropic rotational diffusion is considered, the orientation of the diffusion tensor relative to the molecular dipole moment and additionally the amount of anisotropy in the rotational diffusion constants determine the detailed shape of the nonlinear response. In this case, the height of the observed hump is found to increase with increasing 'diffusional anisotropy'. We discuss our results in relation to the features observed experimentally in supercooled liquids.