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Self-consistent theory for systems with mesoscopic fluctuations.

A Ciach1, W T Góźdź

  • 1Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|August 23, 2016
PubMed
Summary
This summary is machine-generated.

We developed a theory for inhomogeneous systems incorporating mesoscopic fluctuations. This theory accurately predicts 1D model properties and reveals distinct fluctuation effects in 3D systems, impacting compressibility and correlations.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Theoretical Chemistry

Background:

  • Inhomogeneous systems present challenges for theoretical modeling.
  • Mesoscopic fluctuations significantly influence system properties.
  • Understanding particle interactions is crucial for predicting phase behavior.

Purpose of the Study:

  • To develop a theory for inhomogeneous systems including mesoscopic fluctuations.
  • To analyze the impact of fluctuations on correlation and direct correlation functions.
  • To investigate the behavior of one-dimensional (1D) and three-dimensional (3D) models with specific interaction potentials.

Main Methods:

  • Developed a hierarchy of equations for correlation functions.
  • Introduced an approximation for a closed set of self-consistent equations.
  • Numerically solved these equations for 1D and 3D models.
  • Compared theoretical predictions with exact results for the 1D model.

Main Results:

  • The theory shows qualitative agreement with exact 1D results; semi-quantitative agreement in the simplest form.
  • Fluctuation effects in 3D models differ significantly, despite similar mean-field behavior.
  • Both 3D models exhibit large-small-large compressibility sequences with increasing particle density.
  • Observed oscillatory correlation decay and large correlation lengths associated with low compressibility.
  • One 3D model shows temperature-dependent compressibility changes and van der Waals loops.

Conclusions:

  • The developed theory provides a framework for studying inhomogeneous systems with mesoscopic fluctuations.
  • Fluctuations play a critical role in determining the properties of 3D systems, leading to complex compressibility behavior.
  • Further research is needed to fully characterize the strongly inhomogeneous phase in 3D systems.