Large deviations and transitions between equilibria for stochastic Landau-Lifshitz-Gilbert equation

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JournalArchive for Rational Mechanics and Analysis
DateAccepted/In press - 8 Apr 2017
DateE-pub ahead of print - 28 Apr 2017
DatePublished (current) - Nov 2017
Issue number2
Pages (from-to)497–558
Early online date28/04/17
Original languageEnglish


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.

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    Research areas

  • stochastic Landau-Lifschitz equation, strong solutions, maximal regularity, large deviations, Freidlin-Ventzell estimates

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