Condensed Matter > Statistical Mechanics
[Submitted on 1 Dec 2016 (v1), last revised 5 Apr 2017 (this version, v3)]
Title:The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels
View PDFAbstract:Weyl-Heisenberg ensembles are a class of determinantal point processes associated with the Schrödinger representation of the Heisenberg group. Hyperuniformity characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. We will prove that Weyl-Heisenberg ensembles are hyperuniform. Weyl-Heisenberg ensembles include as a special case a multi-layer extension of the Ginibre ensemble modeling the distribution of electrons in higher Landau levels, which has recently been object of study in the realm of the Ginibre-type ensembles associated with polyanalytic functions. In addition, the family of Weyl-Heisenberg ensembles includes new structurally anisotropic processes, where point-statistics depend on the different spatial directions, and thus provide a first means to study directional hyperuniformity.
Submission history
From: José Luis Romero [view email][v1] Thu, 1 Dec 2016 17:37:47 UTC (39 KB)
[v2] Wed, 1 Mar 2017 11:29:12 UTC (40 KB)
[v3] Wed, 5 Apr 2017 15:40:23 UTC (30 KB)
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