Dynamics and thermodynamics of systems with long-range dipole-type interactions

Area of Science:

• Statistical Mechanics
• Computational Physics
• Complex Systems

Background:

• Systems with long-range interactions exhibit complex dynamics.
• Understanding quasistationary states is crucial for characterizing non-equilibrium systems.

Purpose of the Study:

• To propose and analyze a Hamiltonian mean field model with dipole-dipole interactions.
• To investigate the dynamics and thermodynamics of systems with long-range interactions.

Main Methods:

• Analytical derivation of equilibrium from the canonical ensemble.
• Molecular dynamics simulations (microcanonical ensemble).
• Analysis of kinetic energy evolution and quasistationary states.

Main Results:

• Two sequential plateaus (quasistationary states) observed in finite systems.
• The first plateau decays into a second, distinct quasistationary state.
• The lifetime of the first plateau follows a power law dependence on system size (N).

Conclusions:

• The proposed model accurately captures dynamics leading to equilibrium.
• Finite-size effects are significant, leading to distinct quasistationary states.
• In the thermodynamic limit, the system is expected to exhibit a single quasistationary state.