The Widom-Rowlinson model: Mesoscopic fluctuations for the critical droplet
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866911509694644224 |
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| author | Hollander, Frank den Jansen, Sabine Kotecký, Roman Pulvirenti, Elena |
| author_facet | Hollander, Frank den Jansen, Sabine Kotecký, Roman Pulvirenti, Elena |
| contents | We study the critical droplet for a close-to-equilibrium Widom-Rowlinson model of interacting particles, represented by disks of radius $1$, in the two-dimensional plane at low temperature. The critical droplet is the set of macroscopic states that correspond to saddle points for the passage from a low-density supersaturated vapour to a stable high-density liquid. We analyse the mesoscopic fluctuations of the surface of the critical droplet, which turns out to be the set of particle configurations that are close to a disk of a certain deterministic radius. Our results represent the first detailed rigorous analysis of the surface fluctuations of a continuum interacting particle system exhibiting condensation and, as such, constitute a fundamental step in the study of phase separation from the perspective of stochastic geometry. At the same time, our results serve as a basis for the study of a non-equilibrium version of the Widom-Rowlinson model, to be analysed elsewhere, where they lead to a correction term in the Arrhenius formula for the average vapour-liquid crossover time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_00453 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The Widom-Rowlinson model: Mesoscopic fluctuations for the critical droplet Hollander, Frank den Jansen, Sabine Kotecký, Roman Pulvirenti, Elena Mathematical Physics 60J45, 60J60, 60K35, 82C21, 82C22, 82C27 We study the critical droplet for a close-to-equilibrium Widom-Rowlinson model of interacting particles, represented by disks of radius $1$, in the two-dimensional plane at low temperature. The critical droplet is the set of macroscopic states that correspond to saddle points for the passage from a low-density supersaturated vapour to a stable high-density liquid. We analyse the mesoscopic fluctuations of the surface of the critical droplet, which turns out to be the set of particle configurations that are close to a disk of a certain deterministic radius. Our results represent the first detailed rigorous analysis of the surface fluctuations of a continuum interacting particle system exhibiting condensation and, as such, constitute a fundamental step in the study of phase separation from the perspective of stochastic geometry. At the same time, our results serve as a basis for the study of a non-equilibrium version of the Widom-Rowlinson model, to be analysed elsewhere, where they lead to a correction term in the Arrhenius formula for the average vapour-liquid crossover time. |
| title | The Widom-Rowlinson model: Mesoscopic fluctuations for the critical droplet |
| topic | Mathematical Physics 60J45, 60J60, 60K35, 82C21, 82C22, 82C27 |
| url | https://arxiv.org/abs/1907.00453 |