Anomalous behavior of the Kramers rate at bifurcations in classical field theoriesReport as inadecuate




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1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans 2 FRDP - Fédération de recherche Denis Poisson 3 Faculty of Mathematics Bielefeld

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.

Keywords : Kramers rate Ginzburg-Landau equation space-time white noise metastability activation energy transition states potential theory





Author: Nils Berglund - Barbara Gentz -

Source: https://hal.archives-ouvertes.fr/



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