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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
70/2005

Tunneling in two dimensions

Giovanni Bellettini, Anna De Masi, Nicolas Dirr and Errico Presutti

Abstract

Tunnelling is studied here as a variational problem formulated in terms of a functional which approximates the rate function for large deviations in Ising systems with Glauber dynamics and Kac potentials. The spatial domain is a two-dimensional square of side $L$ with reflecting boundary conditions. For $L$ large enough the penalty for tunnelling from the minus to the plus equilibrium states is determined. Minimizing sequences are fully characterized and shown to have approximately a planar symmetry at all times, thus departing from the Wulff shape in the initial and final stages of the tunnelling.

Received:
Jul 11, 2005
Published:
Jul 11, 2005
MSC Codes:
82C05, 60F10
Keywords:
large deviations, nonlocal evolution equation, tunneling

Related publications

inJournal
2007 Repository Open Access
Giovanni Bellettini, Anna De Masi, Nicolas Dirr and Errico Presutti

Tunneling in two dimensions

In: Communications in mathematical physics, 269 (2007) 3, pp. 715-763