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Nonlinear Langevin equations and the time dependent density functional method.

A Yoshimori1

  • 1Department of Physics, Kyushu University, Fukuoka 812-8581, Japan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary
This summary is machine-generated.

This study reformulates streaming velocity terms in nonlinear Langevin equations to clarify their role in time-dependent density functional methods (TDDFM). Careful derivation is needed as only specific terms introduce TDDFM.

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Area of Science:

  • Theoretical Chemistry
  • Statistical Mechanics
  • Computational Physics

Background:

  • Nonlinear Langevin equations are fundamental in statistical mechanics.
  • Mori's projection operator method yields various nonlinear Langevin equations based on phase space function choices.
  • Understanding the streaming velocity term is crucial for accurate modeling.

Purpose of the Study:

  • To reformulate the two streaming velocity terms in the nonlinear Langevin equation.
  • To analyze the contribution of these terms to the time-dependent density functional method (TDDFM).
  • To provide guidance on the careful derivation of TDDFM.

Main Methods:

  • Reformulation of streaming velocity terms within the nonlinear Langevin equation framework.
  • Application of Mori's projection operator method.
  • Analysis of phase space function dependencies.

Main Results:

  • Identified an invariable form of the streaming velocity term, independent of certain phase space functions.
  • Demonstrated that this invariable term does not introduce TDDFM.
  • Showed that linearization of the second streaming velocity term aligns with the linear Langevin equation's frequency term.

Conclusions:

  • The derivation of time-dependent density functional methods (TDDFM) requires careful consideration of streaming velocity terms.
  • Only specific streaming velocity terms contribute to TDDFM.
  • Awareness of these distinctions is vital for accurate theoretical development.