Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert Equation

Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

Large Deviations and Transitions Between Equilibria for Stochastic Landau–Lifshitz–Gilbert Equation

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-017-1117-0
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Apr 28, 2017

References

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