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Structural degeneracy in pair distance distributions
Frank H Stillinger1, Salvatore Torquato2
1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.
The Journal of Chemical Physics
|June 3, 2019
Summary
Many-particle systems can have identical pair distances but different configurations. This study explores how subtle three-particle interactions can alter system properties without affecting pair distances, remaining undetected by standard methods.
Area of Science:
- Statistical Mechanics
- Computational Physics
- Condensed Matter Physics
Background:
- Interparticle pair distances traditionally describe many-particle systems.
- These distances determine pressure and mean energy for simple systems.
- However, multiple configurations can yield the same pair distance distribution.
Purpose of the Study:
- To investigate how configuration details are overlooked in many-particle systems.
- To analyze configurational degeneracy and its implications.
- To explore the existence of "pair-invisible" interactions.
Main Methods:
- Analysis of small-system examples with configurational pattern ambiguity.
- Concentration on large-system classical canonical ensembles.
- Examination of two-dimensional systems for triangle shape and chirality distribution.
- Exploration of three-dimensional systems with potential three-particle interactions.
Main Results:
- Full pair distance specification can still allow for distinct configurational pattern ambiguity.
- Configurational degeneracy in 2D systems is analyzed, with chirality controlled by three-particle interactions.
- The existence of three-particle interactions that modify the three-particle distribution function but not the pair distribution function is explored.
Conclusions:
- Subtle interactions can influence many-particle system configurations in ways not detectable by pair distance analysis.
- Conventional diffraction experiments may miss crucial information about system structure.
- Understanding these "pair-invisible" interactions is vital for a complete description of many-particle systems.
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