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Anomalous behavior of the Kramers rate at bifurcations in classical field theories

Abstract : We consider a Ginzburg-Landau partial differential equation in a bounded interval, perturbed by weak spatio-temporal noise. As the interval length increases, a transition between activation regimes occurs, in which the classical Kramers rate diverges [R.S. Maier and D.L. Stein, Phys. Rev. Lett. 87, 270601 (2001)]. We determine a corrected Kramers formula at the transition point, yielding a finite, though noise-dependent prefactor, confirming a conjecture by Maier and Stein [vol. 5114 of SPIE Proceeding (2003)]. For both periodic and Neumann boundary conditions, we obtain explicit expressions of the prefactor in terms of Bessel and error functions.
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Submitted on : Tuesday, January 6, 2009 - 3:23:53 PM
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Nils Berglund, Barbara Gentz. Anomalous behavior of the Kramers rate at bifurcations in classical field theories. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 42 (5), pp.052001. ⟨10.1088/1751-8113/42/5/052001⟩. ⟨hal-00321846v2⟩

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