HAL: hal-00321846, version 2

arXiv: 0809.2652

DOI: 10.1088/1751-8113/42/5/052001

Detailed view

Export this paper BibTeX - EndNote - TEI - RefWorks -

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

Available versions:

v1 (2008-09-16)

v2 (2009-01-06)

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

Nils Berglund 1, Barbara Gentz 2

(2009-01-06)

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.

1:	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349
2:	Faculty of Mathematics, University of Bielefeld
	Universität Bielefeld

Subject

:

Mathematics/Probability Physics/Condensed Matter/Mesoscopic Systems and Quantum Hall Effect

Keyword(s): Kramers rate – Ginzburg-Landau equation – space-time white noise – metastability – activation energy – transition states – potential theory

hal-00321846, version 2

http://hal.archives-ouvertes.fr/hal-00321846

oai:hal.archives-ouvertes.fr:hal-00321846

From: Nils Berglund <>

Submitted on: Tuesday, 6 January 2009 15:23:53

Updated on: Friday, 9 January 2009 13:40:39