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

TL;DR

This paper extends nonlinear response theory for Markovian stochastic reorientations of molecules, analyzing how anisotropy and jump models affect susceptibility features, with implications for understanding supercooled liquids.

Contribution

It introduces extended models of anisotropic rotational diffusion and jump processes, analyzing their nonlinear susceptibilities up to fifth order.

Findings

Hump in nonlinear susceptibility depends on model parameters.

Anisotropy increases the height of the susceptibility hump.

Modeling of external field coupling influences the response shape.

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.