Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Theoretical Chemistry

Background:

• Mode-coupling theory (MCT) has historically described dense fluids and the glass transition.
• MCT's approximations limit its accuracy and correction mechanisms.

Purpose of the Study:

• To explore the kinetics of classical particles using a new first-principles theoretical framework.
• To provide a full solution for hard spheres under Smoluchowski dynamics.

Main Methods:

• Developed a new theory from first principles using a self-consistent perturbation expansion.
• Numerically solved the kinetic equation for the density-density time correlation function.
• Applied asymptotic approximation techniques to fit solutions and extract critical parameters.

Main Results:

• Observed the characteristic two-step decay and ergodic-nonergodic transition in supercooled fluids.
• Achieved high precision over a wide range of time and wave-number, tracking solutions near the transition.
• Found qualitative agreement with known glassy behavior and limited quantitative agreement with experiments.

Conclusions:

• The new theory reproduces key features of glassy systems seen in other approaches.
• It offers advantages of being derived from first principles and allowing systematic corrections.
• This framework advances the understanding of fluid-to-glass transitions.