Lattice melting and rotation in perpetually pulsating equilibria

Area of Science:

• Astrophysics and computational physics
• Statistical mechanics

Background:

• Systems with r^{-2} and r^{2} potential energies exhibit unique dynamical behaviors.
• Violent relaxation is absent, leading to persistent pulsations.

Purpose of the Study:

• Investigate the long-term behavior of systems with specific potential energies.
• Characterize lattice formation, disintegration, and phase transitions.
• Analyze the dynamics of rotating pulsating equilibria and their discrete counterparts.

Main Methods:

• Numerical simulations of systems with r^{-2} and r^{2} potential energies.
• Analysis of lattice structures and their stability.
• Comparison of fluid and discrete system dynamics.

Main Results:

• Systems form lattices at low nonpulsational energy, which disintegrate as energy increases.
• Observed a halving of specific heats during the solid-to-fluid transition.
• Lattice structures evolve from N=18 configurations to hexagonal close-packed for large N, forming shell structures.
• Large N behavior is analogous to a gamma=5/3 polytropic fluid under quasigravity.

Conclusions:

• Pulsating systems do not reach Virial equilibrium but can form stable, albeit pulsating, structures.
• The study provides insights into phase transitions and structural evolution in self-gravitating systems.
• Comparison of fluid and discrete systems reveals differences in angular momentum redistribution and mixing rates.