Symplectic integrators for spin systems

Abstract

We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in ${\mathbb{R}}^3$. Unlike splitting methods, it is defined for all Hamiltonians, and is $O(3)$-equivariant. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields an integrable discretization of the reduced motion of a free rigid body.

References in corpus (3)

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• Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries
• On post-Newtonian orbits and the Galactic-center stars

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• Secular Dynamics around a Supermassive Black Hole via Multipole Expansion
• Accelerating spin-space sampling by auxiliary spin-dynamics and temperature-dependent spin-cluster expansion
• Influence of round-off errors on the reliability of numerical simulations of chaotic dynamic systems
• Geometry of discrete-time spin systems
• Integrability of point-vortex dynamics via symplectic reduction: a survey
• Clean Numerical Simulation: A New Strategy to Obtain Reliable Solutions of Chaotic Dynamic Systems