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

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.

17 pages, 6 figures

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Cited by in corpus (6)

• Dynamic facilitation theory: A statistical mechanics approach to dynamic arrest
• Unifying different interpretations of the nonlinear response in glass-forming liquids
• Modeling non-linear dielectric susceptibilities of supercooled molecular liquids
• Third and Fifth Harmonic Responses in Viscous Liquids
• Nonlinear response theory for Markov processes III: Stochastic models for dipole reorientations
• Nonlinear response theory for Markov processes IV: The asymmetric double well potential model revisited