English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This is the first in a series of three papers in which we study atwo-dimensional lattice gas consisting of two types of particles subject toKawasaki dynamics at low temperature in a large finite box with an openboundary. Each pair of particles occupying neighboring sites has a negativebinding energy provided their types are different, while each particle has apositive activation energy that depends on its type. There is no binding energybetween neighboring particles of the same type. At the boundary of the boxparticles are created and annihilated in a way that represents the presence ofan infinite gas reservoir. We start the dynamics from the empty box and computethe transition time to the full box. This transition is triggered by a\emph{critical droplet} appearing somewhere in the box.  We identify the region of parameters for which the system is metastable. Forthis region, in the limit as the temperature tends to zero, we show that thefirst entrance distribution on the set of critical droplets is uniform, computethe expected transition time up to a multiplicative factor that tends to one,and prove that the transition time divided by its expectation is exponentiallydistributed. These results are derived under \emph{three hypotheses} on theenergy landscape, which are verified in the second and the third paper for acertain subregion of the metastable region. These hypotheses involve threemodel-dependent quantities -- the energy, the shape and the number of thecritical droplets -- which are identified in the second and the third paper aswell.

Metastability for Kawasaki dynamics at low temperature with two types of particles