Anomalous behavior of the Kramers rate at bifurcations in classical field theories
Berglund, Nils
Berglund
Nils
Gentz, Barbara
Gentz
Barbara
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 (Maier and Stein 2001 Phys. Rev. Lett. 87 270601). We determine a corrected Kramers formula at the transition point, yielding a finite, though noise-dependent, rate prefactor, confirming a conjecture by Maier and Stein ( 2003 SPIE Proc. vol 5114 pp 67-78). For both periodic and Neumann boundary conditions, we obtain explicit expressions for the prefactor in terms of Bessel and error functions.
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2009