三维环境中平面磁矩的随机动力学
Stochastic dynamics of planar magnetic moments in a three-dimensional environment
摘要：
本文研究了嵌入三维环境中的二维磁矩的随机动力学，该动力学由随机Landau-Lifshitz-Gilbert（sLLG）方程描述。我们定义了这个方程的协变推广，有效的“广义Stratonovich离散化处方”。我们提出了一个路径积分公式，允许计算任何$n-$点关联函数，独立于所使用的随机微积分。使用这种形式主义，我们证明了向量噪声的carnival制定之间的等价性，只有一个标量波动项的极坐标制定。特别是，我们表明，各向同性的波动，该系统是由一个{ \em添加剂随机过程}，尽管乘法项出现在原来的制定sLLG方程，但是，各向异性波动的噪声原来是真正的乘法。
英文摘要：
We study the stochastic dynamics of a two-dimensional magnetic moment embedded in a three-dimensional environment, described by means of the stochastic Landau-Lifshitz-Gilbert (sLLG) equation. We define a covariant generalization of this equation, valid in the "generalized Stratonovich discretization prescription". We present a path integral formulation that allows to compute any $n-$point correlation function, independently of the stochastic calculus used. Using this formalism, we show the equivalence between the cartesian formulation with vectorial noise, with the polar formulation with just one scalar fluctuation term. In particular, we show that, for isotropic fluctuations, the system is represented by an {\em additive stochastic process}, despite of the multiplicative terms appearing in the original formulation of the sLLG equation, but, for anisotropic fluctuations the noise turns out to be truly multiplicative.
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