Long-range interacting particles on a helix: A statistical and correlation analysis of equilibrium configurations

Area of Science:

• Classical mechanics
• Statistical physics
• Condensed matter physics

Background:

• Understanding few-body systems is crucial in physics.
• Repulsive forces in confined systems present unique challenges.
• Helical manifolds offer a novel geometry for studying particle interactions.

Purpose of the Study:

• To analyze the spatial and energetic properties of equilibrium configurations.
• To investigate how system size affects particle arrangement and energy.
• To explore the interplay between repulsive forces and helical confinement.

Main Methods:

• Statistical and correlational analysis.
• Examination of systems with two to eight equally charged classical particles.
• Focus on equilibrium configurations within a one-dimensional helical manifold.

Main Results:

• The two-body system exhibits an oscillatory effective potential, creating stable equilibria.
• The number of equilibria increases with system size, following a power-law.
• A transition from spatial regularity to disorder is observed as particles are added, with interparticle distances clustering around helical winding multiples.

Conclusions:

• The complexity of the potential energy surface drives the increase in equilibria.
• Despite increased disorder, an underlying regularity persists due to helical geometry and particle repulsion.
• An energetic hierarchy of equilibria emerges, with increasing fluctuations at larger system sizes.