2023/04/27 by Simone Baldassarri, Alexandre Gaudillière, Baldassarri, Simone +9
Materials Science · Mathematics · Physics and Astronomy · #60K35 #82C26 #82C27 #FOS: Mathematics #FOS: Physical sciences #Material Dynamics and Properties #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2304.14099
openalex publication_date 2023/04/27 · openalex created_date 2023/04/30 · openalex updated_date 2026/08/01
This is the second in a series of three papers in which we study a lattice gas subject to Kawasaki conservative dynamics at inverse temperature β>0 in a large finite box Λβ⊂\mathbb Z2 whose volume depends on β. Each pair of neighbouring particles has a negative binding energy -U<0, while each particle has a positive activation energy Δ>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 Δ∈(U,2U) and in the limit as β→∞, how and when the system nucleates. In the first paper we showed that subcritical droplets behave as quasi-random walks. In the present paper we use the results in the first paper to analyse how subcritical droplets form and dissolve on multiple space-time scales when the volume is moderately large, i.e., |Λβ|=\mathrm eΘβ with Δ<Θ<2Δ-U. In the third paper we consider the setting where the volume is very large, namely, |Λβ|=\mathrm eΘβ with Δ<Θ<Γ-(2Δ-U), where Γ is the energy of the critical droplet in the local model with fixed volume, and use the results in the first two papers to identify the nucleation time. We will see that in a very large volume critical droplets appear more or less independently in boxes of moderate volume, a phenomenon referred to as homogeneous nucleation. Since Kawasaki dynamics is conservative, i.e., particles are preserved, we need to control non-local effects in the way droplets are formed and dissolved. This is done via a deductive approach: the tube of typical trajectories leading to nucleation is described via a series of events on which the evolution of the gas consists of droplets wandering around on multiple space-time scales.