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Updated: Mar 16, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Self-consistent theory for systems with mesoscopic fluctuations
1Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland.
Summary
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.
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.
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