Kinetic density functional theory of freezing

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Understanding the freezing transition in dense hard sphere systems is crucial for statistical mechanics.
• Existing theories often struggle to accurately capture the complex dynamics and structural correlations involved.

Purpose of the Study:

• To present a novel theoretical framework for the freezing of dense hard sphere gases.
• To develop hydrodynamic equations that incorporate non-local density variations and structural correlations.

Main Methods:

• Utilized a revised Enskog theory as the starting point.
• Employed a modified Chapman-Enskog procedure to derive hydrodynamic equations.
• Incorporated structural correlations into the derived equations.
• Performed analysis and numerical simulations to validate the theory.

Main Results:

• Derived hydrodynamic equations that effectively function as a time-dependent density functional theory.
• Successfully captured the solid-liquid phase transition in dense hard sphere systems.
• Demonstrated the importance of retaining structural correlations for accurate phase transition prediction.

Conclusions:

• The developed theory provides a robust method for describing the freezing of dense hard sphere gases.
• The approach effectively bridges hydrodynamic descriptions with density functional theory.
• Numerical simulations confirm the theory's capability in predicting phase transitions.