Large deviations for a stochastic Landau-Lifshitz equation, extended version

Details Large deviations for a stochastic Landau-Lifshitz equation, extended version Large deviations for a stochastic Landau-Lifshitz equation, extended version

2012-02-02

arxiv.org/abs/1202.0370v1

Mathematics

Probability

78 pages, 0 figures

Scientific paper

We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise; this could be a simple model of magnetization in a needle-shaped domain in magnetic media. After showing that a unique, regular solution exists, we obtain a large deviation principle for small noise asymptotics of solutions using the weak convergence method. We then apply the large deviation principle to show that small noise in the field can cause magnetization reversal and also to show the importance of the shape anisotropy parameter for reducing the disturbance of the magnetization caused by small noise in the field.

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