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

Berglund N, Gentz B (2009)
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42(5).

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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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Zeitschriftentitel
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Band
42
Ausgabe
5
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Berglund N, Gentz B. Anomalous behavior of the Kramers rate at bifurcations in classical field theories. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2009;42(5).
Berglund, N., & Gentz, B. (2009). Anomalous behavior of the Kramers rate at bifurcations in classical field theories. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 42(5). doi:10.1088/1751-8113/42/5/052001
Berglund, N., and Gentz, B. (2009). Anomalous behavior of the Kramers rate at bifurcations in classical field theories. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42.
Berglund, N., & Gentz, B., 2009. Anomalous behavior of the Kramers rate at bifurcations in classical field theories. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 42(5).
N. Berglund and B. Gentz, “Anomalous behavior of the Kramers rate at bifurcations in classical field theories”, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 42, 2009.
Berglund, N., Gentz, B.: Anomalous behavior of the Kramers rate at bifurcations in classical field theories. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 42, (2009).
Berglund, Nils, and Gentz, Barbara. “Anomalous behavior of the Kramers rate at bifurcations in classical field theories”. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42.5 (2009).