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2012 Metastability for Kawasaki dynamics at low temperature with two types of particles
Frank den Hollander, Francesca Nardi, Alessio Troiani
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Electron. J. Probab. 17: 1-26 (2012). DOI: 10.1214/EJP.v17-1693


This is the first in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics atlow temperature in a large finite box with an open boundary. Each pair of particlesoccupying neighboring sites has a negative binding energy provided their types aredifferent, while each particle has a positive activation energy that depends onits type. There is no binding energy between neighboring particles of the same type.At the boundary of the box particles are created and annihilated in a way thatrepresents the presence of an infinite gas reservoir. We start the dynamics from the empty box and compute the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box. We identify the region of parameters for which the system is metastable. For thisregion, in the limit as the temperature tends to zero, we show that the firstentrance distribution on the set of critical droplets is uniform, compute theexpected transition time up to a multiplicative factor that tends to one, and prove that the transition time divided by its expectation is exponentially distributed. These results are derived under three hypotheses on the energy landscape, which are verified in the second and the third paper for a certain subregion of the metastable region. These hypotheses involve three model-dependent quantities - the energy, the shape and the number of the critical droplets - which are identified in the second and the third paper as well.


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Frank den Hollander. Francesca Nardi. Alessio Troiani. "Metastability for Kawasaki dynamics at low temperature with two types of particles." Electron. J. Probab. 17 1 - 26, 2012.


Accepted: 1 January 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1246.60119
MathSciNet: MR2869249
Digital Object Identifier: 10.1214/EJP.v17-1693

Primary: 60K35
Secondary: 82C26

Keywords: capacity , critical droplet , Dirichlet form , Kawasaki dynamics , metastable region , Metastable transition time , Multi-type particle systems , potential theory


Vol.17 • 2012
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