# Nonlinear response theory for Markov processes II: Fifth-order response functions

## TL;DR

This paper extends nonlinear response theory for Markov processes to fifth-order, analyzing higher-order susceptibilities in models of dipole reorientations and trap models, revealing characteristic temperature regimes and the importance of variable coupling.

## Contribution

It introduces fifth-order response calculations for stochastic models, providing new insights into nonlinear susceptibilities and their temperature dependence in glassy systems.

## Key findings

- Humps observed in higher-order susceptibilities for most models.
- Two characteristic temperature regimes for the asymmetric double well potential.
- Susceptibility behavior depends on the variable coupled to the field.

## Abstract

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. E{\bf 85}, 051502 (2012)). For sinusoidal fields the $5\om$-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.