Nonlinear Dielectric and KERR Effect Relaxation in Alternating Fields

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature T_{0} determined by the value of the asymmetry. In a narrow temperature range around T_{0}, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than T_{0}), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.

Section: Nonlinear Response Theory For Markov Processesmentioning

confidence: 99%

“…refs. [40,41,42,43]. In addition, approximate nonlinear response theory has been investigated more generally [44] and also fluctuation-dissipation relations beyond the linear regime have been discussed [45,46].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear response theory for Markov processes: Simple models for glassy relaxation

Diezemann

2012

“…It is thus assumed that the origin of the hump is intimately related to the existence of a growing amorphous order or some kind of domain structure. On the other hand, it has been argued that the reorientational motion of individual molecules gives rise to a monotonous decay of the modulus from a finite low-frequency value to zero at high frequencies and this behavior is found for the model of isotropic rotational diffusion [17,18,19,20]. It is, however, to be mentioned that also some models lacking spatial correlations like the Box model and variations of this and other phenomenological models have been shown to exhibit a hump in the nonlinear susceptibilities [14,21,22,23].…”

Section: Introductionmentioning

confidence: 99%

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

Diezemann¹

2018

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. E85, 051502 (2012), Phys. Rev. E96, 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. PACS: 64.70.Q-, 61.20.Lc, 05.40.-a 1 arXiv:1808.03188v2 [cond-mat.soft]

“…The nonlinear response theory of dipole reorientations has been worked out for various models already some time ago [22,23,24,25] and has also been extended to include longrange dipolar interactions [26]. In ref.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear response theory for Markov processes. II. Fifth-order response functions

Diezemann¹

2017

The nonlinear response of stochastic models obeying a master equation is calculated up to fifth-order in the external field thus extending the third-order results obtained earlier (G. Diezemann, Phys. Rev. E85, 051502 (2012)). For sinusoidal fields the 5ω-component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurence of such a hump as compared to a single characteristic regime in case of the third-order response. In case of the trap model the results strongly depend on the variable coupled to the field. As for the third-order response, the low-frequency limit of the susceptibility plays a crucial role with respect to the occurence of a hump. The findings are discussed in light of recent experimental results obtained for supercooled liquids. The differences found for the third-order and the fifth-order response indicate that nonlinear response functions might serve as a powerful tool to discriminate among the large number of existing models for glassy relaxation.