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Studying Large Amplitude Oscillatory Shear Response of Soft Materials

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Published on: April 25, 2019

Nonlinear response theory for Markov processes: simple models for glassy relaxation.

Gregor Diezemann¹

¹Institut für Physikalische Chemie, Universität Mainz, Jakob-Welder-Weg 11, 55128 Mainz, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This study formulates nonlinear response theory for Markov processes. It reveals unique temperature-dependent behaviors in dielectric spectroscopy models and highlights the influence of variable choice on nonlinear response functions in glasses.

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Area of Science:

Physics
Physical Chemistry
Statistical Mechanics

Background:

Nonlinear response theory is crucial for understanding complex systems.
Markov processes and master equations are fundamental in describing system dynamics.
Dielectric spectroscopy often employs models like asymmetric double-well potentials.

Purpose of the Study:

To formulate a theory for nonlinear response of Markov processes.
To investigate nonlinear dielectric response in an asymmetric double-well potential model.
To analyze nonlinear response in a trap model with Gaussian density of states.

Main Methods:

Time-dependent perturbation theory for Green's functions.
Calculation of response functions up to third order in the external field.
Analysis of frequency and temperature dependencies of nonlinear response.

Main Results:

Static nonlinear response is finite except at a specific temperature T₀.
Cubic response exhibits a peak near the relaxation rate around T₀.
Nonlinear response strongly depends on the choice of dynamical variables in the trap model.

Conclusions:

The study provides a theoretical framework for nonlinear response in complex systems.
Specific temperature dependencies and frequency behaviors of nonlinear response were identified.
The choice of dynamical variables significantly impacts nonlinear response functions, relevant for supercooled liquids and glasses.