The Weyl-Heisenberg ensemble: Hyperuniformity and higher Landau levels

L. D. Abreu, J. M. Pereira, J. L. Romero, S. Torquato

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23 Scopus citations


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.

Original languageEnglish (US)
Article number043103
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number4
StatePublished - Apr 20 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • correlation functions
  • fluctuation phenomena
  • matrix models
  • quantum chaos


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