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

Nils Berglund and Barbara Gentz
J. Phys. A: Math. Theor. 42:052001 (2009)
(Fast Track Communication)

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.

PACS numbers: 05.40.-a, 05.45.Yv, 11.10.Wx, 75.60.Jk

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

 

Journal Homepage Published article: 10.1088/1751-8113/42/5/052001 MR2525368 Zbl1155.70016

PDF file (196 Kb) hal-00321846 arXiv/0809.2652