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Updated: Jan 8, 2026

$Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene$

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Fundamental measure theory for predicting many-body correlation functions.

Ilian Pihlajamaa¹, Teunike A van de Pol¹, Liesbeth M C Janssen^1,2

¹Eindhoven University of Technology, Soft Matter and Biological Physics, Department of Applied Physics, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.

Physical Review. E

|December 23, 2025

Summary

Fundamental Measure Theory (FMT) accurately models many-body correlations in hard-sphere fluids. It simplifies complex four-point correlations and captures structural changes in supercooled liquids.

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Area of Science:

Statistical Mechanics
Soft Matter Physics
Computational Physics

Background:

Understanding many-body correlation functions is crucial for describing the behavior of fluids.
Fundamental Measure Theory (FMT) provides a framework for studying these correlations.
Comparing theoretical predictions with simulation data is essential for validating models.

Purpose of the Study:

To evaluate the accuracy of various Fundamental Measure Theory (FMT) formulations in predicting many-body correlation functions.
To compare FMT predictions with Monte Carlo simulations of hard-sphere fluids.
To investigate the contributions to four-point structure factors and their simplification.

Main Methods:

Application of different Fundamental Measure Theory (FMT) formulations.
Performing Monte Carlo simulations of hard-sphere fluids.
Analysis of three- and four-body structure factors and correlation functions.

Main Results:

FMT accurately captures qualitative behavior of three- and four-body structures, especially at low/intermediate wave vectors.
Quantitative accuracy of FMT varies at higher wave vectors.
Dominant contributions to the four-point structure factor stem from direct triplet correlations, simplifying calculations.
FMT reproduces deviations from convolution approximation in glass-forming liquids, indicating its ability to capture growing multipoint correlations.

Conclusions:

Fundamental Measure Theory (FMT) is a valuable tool for studying many-body correlations in fluids.
FMT's ability to simplify four-point correlation calculations and capture supercooling effects is significant.
Further refinement of FMT may improve quantitative accuracy at higher wave vectors.