Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Physics

Background:

• The glass transition is a fundamental phenomenon in condensed matter physics.
• Mode-coupling theory (MCT) provides a theoretical framework for understanding the glass transition dynamics.
• Simulations are crucial for validating theoretical predictions.

Purpose of the Study:

• To quantitatively compare MCT predictions with simulation results for tagged-particle dynamics near the glass transition.
• To identify the range of applicability and limitations of MCT.
• To investigate the impact of system parameters like polydispersity on the glass transition.

Main Methods:

• Comparison of theoretical predictions from MCT with Newtonian and Brownian dynamics simulations.
• Analysis of tagged-particle density-correlation functions and mean-squared displacement.
• Asymptotic analyses of relaxation curves to determine MCT's applicability range.

Main Results:

• Good agreement between MCT and simulations was achieved after correcting for dynamical length scale and transition density errors.
• Deviations were observed at high densities, small wave vectors, and for mean-squared displacement.
• The study identified error sources related to MCT approximations and static structure assumptions.

Conclusions:

• MCT provides a robust description of glass transition dynamics for quasi-hard spheres within certain parameter ranges.
• Approximations in static structure significantly influence the predicted glass-transition density.
• Small polydispersity in the system has a negligible effect on the observed dynamics.