Structural relaxation in complex liquids: non-Markovian dynamics in a bistable potential

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Physical Chemistry

Background:

• Complex systems exhibit structural relaxation influenced by various noise types.
• Generalized Langevin Equation (GLE) and fractional Gaussian noise (fGn) are advanced models for describing such dynamics.
• Understanding these dynamics is crucial for materials science and biophysics.

Purpose of the Study:

• To calculate the time correlation function for particle distance fluctuations in a bistable potential subjected to fGn.
• To compare theoretical predictions with experimental data from optical Kerr effect measurements.
• To assess the applicability of the GLE formalism with fGn for modeling structural relaxation in complex media.

Main Methods:

• Derivation of a Smoluchowski-type equation from a generalized Langevin equation.
• Analytical calculation of the time correlation function C(t) = .
• Comparison of the time derivative dC(t)/dt with experimental data on liquid crystal dynamics.

Main Results:

• The analytical calculations qualitatively reproduced key features of experimental decay curves.
• Observed power law behavior at short/intermediate times and exponential relaxation at long times.
• The model successfully captures aspects of structural relaxation without explicitly including orientational degrees of freedom.

Conclusions:

• The generalized Langevin equation formalism with fractional Gaussian noise provides a robust framework for modeling structural relaxation in complex condensed phase media.
• The model, originally developed for protein dynamics, shows broader applicability.
• This work bridges theoretical modeling and experimental observations in materials science.