The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels
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.
Keywords
Cite
@article{arxiv.1612.00359,
title = {The Weyl-Heisenberg ensemble: hyperuniformity and higher Landau levels},
author = {Luís Daniel Abreu and João M. Pereira and José Luis Romero and Salvatore Torquato},
journal= {arXiv preprint arXiv:1612.00359},
year = {2017}
}
Comments
17 pages, 2 figures. (Typos corrected.)