Homogeneous nucleation for two-dimensional Kawasaki dynamics

Baldassarri Simone, Leiden University

We study a lattice gas subject to Kawasaki dynamics at inverse temperature $\beta>0$ in a large finite box $\Lambda_\beta \subset \mathbb{Z}^2$ of size $|\Lambda_\beta| = e^{\Theta\beta}$, with $\Theta>0$. Each pair of neighbouring particles has a negative binding energy $-U<0$, while each particle has a positive activation energy $\Delta>0$. The initial configuration is drawn from the grand-canonical ensemble restricted to the set of configurations where all the droplets are subcritical. Our goal is to describe, in the metastable regime $\Delta \in (U,2U)$ and in the limit as $\beta\to\infty$, how and when the system nucleates, i.e., creates a critical droplet somewhere in $\Lambda_\beta$ that subsequently grows by absorbing particles from the surrounding gas. We will see that in a very large volume ($\Theta> 2\Delta-U$) critical droplets appear more or less independently in boxes of moderate volume ($\Theta< 2\Delta-U$), a phenomenon referred to as homogeneous nucleation. This is a joint work with Alexandre Gaudillière, Frank den Hollander, Francesca Romana Nardi, Enzo Olivieri and Elisabetta Scoppola.

Area: IS5 - Metastability (Elena Pulvirenti)

Keywords: Lattice gas; Kawasaki dynamics; metastability; nucleation, critical droplets

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