Divergent four-point dynamic density correlation function of a glassy suspension

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Computational Physics

Background:

• Interacting Brownian particles are fundamental in condensed matter.
• Understanding dynamic density correlation functions is key to material properties.
• Previous models exist for two- and three-point correlations.

Purpose of the Study:

• To investigate a four-point dynamic density correlation function for interacting Brownian particles.
• To apply a recently derived diagrammatic formulation to complex particle dynamics.
• To analyze the behavior of the four-point function near a mode-coupling transition.

Main Methods:

• Utilized a diagrammatic formulation for Brownian particle dynamics.
• Resummed specific classes of diagrams in the correlation function calculation.
• Expressed the four-point function in terms of three-point and two-point correlation functions.

Main Results:

• Derived a formula for the four-point dynamic density correlation function.
• The formula relates to existing three-point susceptibility and two-point correlation functions.
• Observed a divergence in the four-point function at small wave vectors near the mode-coupling transition.

Conclusions:

• The derived four-point correlation function provides insights into particle dynamics.
• The structure of the four-point function aligns with proposed models.
• The observed divergence suggests critical behavior at the mode-coupling transition.