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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Dynamics starting from zero velocities in the classical Coulomb three-body problem.

Mitsusada M Sano¹

¹Graduate School of Human and Environmental Studies, Kyoto University, Sakyo, Kyoto, 606-8501, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 16, 2007

Summary

This study reveals fractal, lobelike structures in binary collision orbits for the Coulomb three-body problem involving H-, He, and Li+. These structures offer insights into symbolic dynamics for atomic and ionic systems.

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Area of Science:

Computational Physics
Quantum Chemistry
Atomic and Molecular Dynamics

Background:

The classical Coulomb three-body problem is fundamental to understanding atomic and ionic interactions.
Previous studies have explored symbolic dynamics, particularly for binary collisions in specific configurations.
Investigating the geometrical structures of these dynamics provides deeper insights into system behavior.

Purpose of the Study:

To perform a qualitative geometrical analysis of the classical Coulomb three-body problem.
To elucidate the geometrical structures of atomic and ionic dynamics (H-, He, Li+) with infinite nuclear mass.
To characterize the distribution of final states, fractal structures, and binary collision orbits.

Main Methods:

Qualitative geometrical analysis of the Coulomb three-body problem.
Treatment of atomic and ionic dynamics (H-, He, Li+) under the infinite nuclear mass approximation.
Elucidation of geometrical dynamics from initial conditions with zero velocities.

Main Results:

The distribution of final states exhibits a fractal structure within the initial condition space.
Binary collision orbits form a distinctive lobelike structure.
This lobelike structure is shown to be fractal and continuously connected to collinear eZe configurations.

Conclusions:

Binary collision orbits possess a fractal, lobelike geometry.
This fractal structure is linked to known symbolic dynamics in collinear configurations.
Both binary and triple-collision orbits are expected to aid in developing symbolic dynamics for systems with zero angular momentum.