McLachlan Robert I, Modin Klas, Verdier Olivier
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):061301. doi: 10.1103/PhysRevE.89.061301. Epub 2014 Jun 13.
We present a symplectic integrator, based on the implicit midpoint method, for classical spin systems where each spin is a unit vector in R{3}. Unlike splitting methods, it is defined for all Hamiltonians and is O(3)-equivariant, i.e., coordinate-independent. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields a new integrable discretization of the spinning top.
我们提出了一种基于隐式中点法的辛积分器，用于经典自旋系统，其中每个自旋是(R^{3})中的单位向量。与分裂方法不同，它适用于所有哈密顿量，并且是(O(3))等变的，即与坐标无关。它是非规范相空间辛映射生成函数的一个罕见例子。它给出了旋转陀螺的一种新的可积离散化。
