Nonlinear response theory for Markov processes IV: The asymmetric double well potential model revisited

Abstract

The dielectric response of non-interacting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double well potential model does not follow the Langevin function and only in the linear regime the standard results are recovered. If a finite asymmetry is assumed, the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and the fifth-order response. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equation for the Brownian motion in a model ADWP behaves very similar to the two-state model for high barriers. For small barriers no clearcut time scale separation between the barrier crossing process and the intra-well relaxation exists and the model exhibits a number of time scales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intra-well transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intra-well transitions play only role at the lowest temperatures.

arXiv comment22 pages, 8 figures, revised version, accepted for publication in Phys. Rev. E

References in corpus (15)

• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers
• Non-linear susceptibility in glassy systems: a probe for cooperative dynamical length scales
• Evidence of growing spatial correlations at the glass transition from nonlinear response experiments
• Minimal model for beta relaxation in viscous liquids
• Nonlinear response theory for Markov processes: Simple models for glassy relaxation
• Mechanical Relaxation in Glasses and at the Glass Transition
• Dynamic force spectroscopy: analysis of reversible bond-breaking dynamics
• Cooperativity and Heterogeneity in Plastic Crystals Studied by Nonlinear Dielectric Spectroscopy
• Response-theory for nonresonant hole burning: Stochastic dynamics
• Nonlinear response theory for Markov processes II: Fifth-order response functions
• Third and Fifth Harmonic Responses in Viscous Liquids
• Modeling non-linear dielectric susceptibilities of supercooled molecular liquids
• Nonlinear response theory for Markov processes III: Stochastic models for dipole reorientations
• Nonlinear response functions in an exponential trap model

Cited by in corpus (1)

• Nonlinear dielectric response in glasses: restoring forces and avoided spin-glass criticality