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Symplectic integrators for spin systems

Authors Robert McLachlan
Klas Modin
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Language en
Subject categories Numerical analysis, Computational physics, Mathematical physics, Non-linear dynamics, chaos


We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in ℝ3. 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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