Secular dynamics of long-range interacting particles on a sphere in the axisymmetric limit

Abstract

We investigate the secular dynamics of long-range interacting particles moving on a sphere, in the limit of an axisymmetric mean field potential. We show that this system can be described by the general kinetic equation, the inhomogeneous Balescu--Lenard equation. We use this approach to compute long-term diffusion coefficients, that are compared with direct simulations. Finally, we show how the scaling of the system's relaxation rate with the number of particles fundamentally depends on the underlying frequency profile. This clarifies why systems with a monotonic profile undergo a kinetic blocking and cannot relax as a whole under $1/N$ resonant effects. Because of its general form, this framework can describe the dynamics of globally coupled classical Heisenberg spins, long-range couplings in liquid crystals, or the orbital inclination evolution of stars in nearly Keplerian systems.

arXiv comment8 pages, 6 figures, submitted to PRL

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Cited by in corpus (8)

• Vector Resonant Relaxation of Stars around a Massive Black Hole
• Anisotropic Mass Segregation in Rotating Globular Clusters
• Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects
• Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction
• A numerical study of stellar discs in galactic nuclei
• Orbital alignment and mass segregation in galactic nuclei via vector resonant relaxation
• Young stellar cluster dilution near supermassive black holes: the impact of Vector Resonant Relaxation on neighbour separation
• Kinetic theory of one-dimensional inhomogeneous long-range interacting $N$-body systems at order $1/N^2$ without collective effects