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

Gregor Diezemann¹

¹Institut für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany.

Physical Review. E

|September 28, 2017

Summary

This study extends nonlinear response calculations for stochastic models to fifth order. The findings, particularly the

Area of Science:

Statistical Physics
Nonlinear Dynamics
Condensed Matter Physics

Background:

Stochastic models are crucial for understanding complex systems.
Previous studies calculated nonlinear response up to third order.
Glassy relaxation models require advanced theoretical tools.

Purpose of the Study:

To extend nonlinear response calculations for stochastic models to fifth order.
To investigate higher-order nonlinear susceptibilities in specific models.
To compare nonlinear response functions for discriminating between glassy relaxation models.

Main Methods:

Master equation approach for stochastic models.
Calculation of nonlinear response up to fifth order in external field.

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Analysis of susceptibility components (e.g., 5ω) for sinusoidal fields.

Main Results:

A hump is observed in higher-order susceptibilities for most model realizations.
Asymmetric double well potential model shows two characteristic temperature regimes for hump occurrence.
Trap model results depend on the field-coupled variable, with low-frequency susceptibility playing a key role.

Conclusions:

Nonlinear response functions, especially fifth-order, can differentiate between various glassy relaxation models.
Observed humps in nonlinear susceptibilities provide insights into supercooled liquid dynamics.
The study highlights the utility of higher-order nonlinear response for theoretical model validation.