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.
Bellettini, G., De Masi, A., Dirr, N., Presutti, E. (2007). Tunneling in two dimensions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 269(3), 715-763 [10.1007/s00220-006-0143-9].
Tunneling in two dimensions
BELLETTINI, GIOVANNI;PRESUTTI, ERRICO
2007-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
