随机Landau-Lifshitz-Gilbert方程平衡点间的大偏差和转移
Large deviations and transitions between equilibria for stochastic Landau-Lifshitz-Gilbert equation
摘要：
研究了有界区间上带有限维噪声的随机Landau-Lifshitz方程。我们首先证明了该方程存在一个路径唯一解，并且该解具有极大正则性。其次，利用弱收敛方法证明了解的小噪声渐近性的大偏差原理。证明的一个重要组成部分是紧凑性，或弱到强的连续性，确定性的朗道-Lifschitz方程的解映射，当被认为是一个外部领域的转换。然后，我们应用这个大偏差的原则，以表明，小的噪音可以导致磁化反转。我们还显示了形状各向异性参数的重要性，以减少由小噪声引起的干扰的解决方案。这个问题的动机是铁磁纳米线的磁性存储器的制造中的应用。这是本文前一版本的更新版本。
英文摘要：
We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise. We first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property. Next, we prove the large deviations principle for small noise asymptotic of solutions using the weak convergence method. An essential ingredient of the proof is compactness, or weak to strong continuity, of the solution map for a deterministic Landau-Lifschitz equation, when considered as a transformation of external fields. We then apply this large deviations principle to show that small noise can cause magnetisation reversal. We also show the importance of the shape anisotropy parameter for reducing the disturbance of the solution caused by small noise. The problem is motivated by applications of ferromagnetic nanowires to the fabrication of magnetic memories. This is an updated version of the previous version of this paper.
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