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Markovian approximation and dynamic density functional theory for classical dense liquids.

Toyonori Munakata1

  • 1Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
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This study presents a new kinetic description for dense liquids by applying a Markovian approximation to the Mori-Fujisaka generalized Langevin equation. This approach systematically derives the Smoluchowski equation and dynamic density functional theory (DDFT) for supercooled liquid dynamics.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Dense liquids present a long-standing challenge in statistical mechanics for kinetic description.
  • Understanding supercooled liquid dynamics and the glass transition is crucial in materials science.

Purpose of the Study:

  • To develop a systematic kinetic theory for dense liquids.
  • To derive the Smoluchowski equation and dynamic density functional theory (DDFT) without further approximations.

Main Methods:

  • Application of a Markovian approximation to the Mori-Fujisaka nonlinear generalized Langevin equation.
  • Systematic derivation of Smoluchowski equation and DDFT.

Main Results:

  • Successfully derived the Smoluchowski equation for interacting many-body systems.

Related Experiment Videos

  • Established a microcanonical dynamic density functional theory (DDFT) for liquid dynamics.
  • The derived DDFT differs from traditional grand-canonical approaches in equilibrium liquid theory.

    • Conclusions:

    • The proposed method offers a robust framework for describing the dynamics of dense and supercooled liquids.
    • The microcanonical DDFT provides a novel perspective for studying equilibrium and non-equilibrium phenomena in liquids.