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Tunneling in Two Dimensions

Bellettini, G., De Masi, A., Dirr, Nicolas P. and Presutti, E. 2006. Tunneling in Two Dimensions. Communications in Mathematical Physics 269 (3) , pp. 715-763. 10.1007/s00220-006-0143-9

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Tunneling 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, [9]. The spatial domain is a two-dimensional square of side L with reflecting boundary conditions. For L large enough the penalty for tunneling 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 tunneling. In a final section (Sect. 11), we extend the results to d = 3 but their validity in d > 3 is still open.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 0010-3616
Last Modified: 04 Jun 2017 02:52

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