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

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

2008-09-16

arxiv.org/abs/0809.2652v2

Journal of Physics A Mathematical and Theoretical 42, 5 (2009) 052001

Mathematics

Probability

Scientific paper

10.1088/1751-8113/42/5/052001

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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