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arXiv · 1612.00359

The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels

Luís Daniel Abreu·João M. Pereira·José Luis Romero·Salvatore Torquato
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Abstract

Weyl-Heisenberg ensembles are a class of determinantal point processes associated with the Schr\"odinger 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.

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Luís Daniel Abreu, João M. Pereira, José Luis Romero, Salvatore Torquato. 2016-12-01. The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels. https://doi.org/10.1088/1742-5468/aa68a7

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