Collisional relaxation in the inhomogeneous Hamiltonian mean-field model: Diffusion coefficients

Area of Science:

• Statistical physics
• Plasma physics
• Astrophysical systems

Background:

• Systems with long-range interactions exhibit quasistationary states (QSS) and slow collisional relaxation.
• Understanding relaxation dynamics is key in fields like plasma physics and gravitational systems.

Purpose of the Study:

• To analyze collisional relaxation in the Hamiltonian mean-field model.
• To compare kinetic equations (Landau and Lenard-Balescu) with and without collective effects.
• To validate theoretical predictions with numerical simulations.

Main Methods:

• Utilized kinetic equations at the 1/N order: Landau equation (neglecting collective effects) and Lenard-Balescu equation (including collective effects).
• Derived explicit expressions for diffusion coefficients for any magnetization.
• Obtained analytic expressions for highly clustered configurations.

Main Results:

• Collective effects are essential for accurately describing the relaxation dynamics in these systems.
• Explicit diffusion coefficients were derived using both kinetic equations.
• Analytic solutions were found for highly clustered configurations.

Conclusions:

• Collective effects play a critical role in the collisional relaxation of systems with long-range interactions.
• The study demonstrates excellent agreement between theoretical predictions from kinetic equations and simulation results.
• This work provides a deeper understanding of non-equilibrium statistical mechanics in Hamiltonian systems.