标题： 非马尔可夫磁化动力学的层次闭合 显示英文标题

标题： Closing the hierarchy for non-Markovian magnetization dynamics

摘要： 我们提出一种随机方法，用于描述纳米磁体磁化时间演化的现象，该方法通过改变噪声的强度，在朗道-利夫希茨-吉尔伯特和朗道-利夫希茨-布洛赫近似之间进行插值。此外，我们考虑噪声的自相关时间，并探讨当其为有限值时对磁化响应尺度的影响，即当其可被描述为有色而非白噪声，以及非马尔可夫特性变得重要时的情况。我们通过引入一个合适的截断方案来闭合磁化矩的层次结构，该方案的有效性通过直接求解矩方程的数值解进行测试，并与从相应随机朗之万方程的数值解中得出的平均值进行比较。这样，我们建立了一个通用框架，既允许粗粒度模拟，又可在本文使用的截断近似之外进行更快的计算。 显示英文摘要

摘要： We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch approximations, by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequences, when it is finite, on the scale of the response of the magnetization, i.e. when it may be described as colored, rather than white, noise and non-Markovian features become relevant. We close the hierarchy for the moments of the magnetization, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the average deduced from a numerical solution of the corresponding stochastic Langevin equation. In this way we establish a general framework, that allows both coarse-graining simulations and faster calculations beyond the truncation approximation used here.