Crystal Ball: A Simple Model for Phase Transitions on a Classical Spherical Lattice

TL;DR

This paper introduces a simple model to study phase transitions in Coulomb systems on spherical lattices, revealing how particle removal can significantly increase kinetic energy, with implications for energy engineering.

Contribution

It develops a framework for simulating Coulomb-coupled particles on a sphere and uncovers a scaling relation for energy gain during phase transitions.

Findings

Significant energy gain observed when increasing removed particles from 1 to 6.

Scaling relation for peak kinetic energy as a function of particle number and removal.

Potential to engineer lattices for maximum energy output.

Abstract

When compressed, certain lattices undergo phase transitions that may allow nuclei to gain significant kinetic energy. To explore the dynamics of this phenomenon, we develop a framework to study Coulomb coupled N-body systems constrained to a parametric surface, focusing specifically on the case of a sphere, as in the Thomson problem. We initialize $N$ total Boron nuclei as point particles on the surface of a sphere, allowing the particles to equilibrate via Coulomb scattering with a viscous damping term. To simulate a phase transition, we remove $N_{rm}$ particles, forcing the system to rearrange into a new equilibrium. We develop a scaling relation for the average peak kinetic energy attained by a single particle as a function of $N$ and $N_{rm}$. For certain values of $N$, we find an order of magnitude energy gain when increasing $N_{rm}$ from 1 to 6, indicating that it may be possible to engineer a lattice that maximizes the energy output.