Large deviations and transitions between equilibria for stochastic Landau-Lifshitz-Gilbert equation. (English) Zbl 1373.35294
Summary: 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 the small noise asymptotic of solutions using the weak convergence method. An essential ingredient of the proof is the 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 from ferromagnetic nanowires to the fabrication of magnetic memories.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
| 60F10 | Large deviations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 35D35 | Strong solutions to PDEs |
| 78A25 | Electromagnetic theory (general) |
| 82D77 | Quantum waveguides, quantum wires |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
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