随机磁化动力学的Nambu力学
Nambu mechanics for stochastic magnetization dynamics
摘要：
Landau-Lifshitz-Gilbert（LLG）方程描述了阻尼磁化矢量的动力学，可以理解为拉莫尔自旋进动的推广。LLG方程不能从哈密顿框架中推导出来，通过引入耦合到通常的浴，但需要引入额外的约束。结果表明，这些约束可以制定优雅和一致的耗散Nambu力学的框架。这对变分原理和控制守恒量的隐藏对称性的拓扑方面都有许多影响。我们特别研究了耗散Nambu力学的阻尼项如何影响磁系统与随机水库的一致性相互作用，并推导出磁化的主方程。这些建议得到了数值研究的支持，使用辛积分保持Nambu方程的拓扑结构。这些结果进行了比较，通过直接采样的随机方程，并通过使用封闭假设的时刻方程，推导出的主方程进行计算。
英文摘要：
The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped magnetization vector that can be understood as a generalization of Larmor spin precession. The LLG equation cannot be deduced from the Hamiltonian framework, by introducing a coupling to a usual bath, but requires the introduction of additional constraints. It is shown that these constraints can be formulated elegantly and consistently in the framework of dissipative Nambu mechanics. This has many consequences for both the variational principle and for topological aspects of hidden symmetries that control conserved quantities. We particularly study how the damping terms of dissipative Nambu mechanics affect the consistent interaction of magnetic systems with stochastic reservoirs and derive a master equation for the magnetization. The proposals are supported by numerical studies using symplectic integrators that preserve the topological structure of Nambu equations. These results are compared to computations performed by direct sampling of the stochastic equations and by using closure assumptions for the moment equations, deduced from the master equation.
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