Symplectic integrators for spin systems

Robert I. McLachlan; Klas Modin; Olivier Verdier

doi:10.1103/physreve.89.061301

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arXiv · 1402.4114

Symplectic integrators for spin systems

Robert I. McLachlan·Klas Modin·Olivier Verdier

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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.

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Robert I. McLachlan, Klas Modin, Olivier Verdier. 2014-10-26. Symplectic integrators for spin systems. https://doi.org/10.1103/physreve.89.061301

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