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Pré-Publication, Document De Travail Année : 2015

The Crystallization Conjecture: A Review

Xavier Blanc

Résumé

In this article we describe the crystallization conjecture. The latter intends to investigate why interacting particles often place themselves into periodic configurations, breaking thereby the natural translation-invariance of the system. This famous problem is still largely open. Mathematically, it amounts to studying the minima of a real-valued function defined on $\mathbb{R}^{3N}$ where $N$ is the number of particles, which tends to infinity. We review the existing literature and mention several related open problems, of which many have not been thoroughly studied.
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Dates et versions

hal-01139322 , version 1 (03-04-2015)
hal-01139322 , version 2 (05-10-2015)

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Xavier Blanc, Mathieu Lewin. The Crystallization Conjecture: A Review. 2015. ⟨hal-01139322v1⟩
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