Abstract
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 language | English (US) |
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Article number | 043103 |
Journal | Journal of Statistical Mechanics: Theory and Experiment |
Volume | 2017 |
Issue number | 4 |
DOIs | |
State | Published - Apr 20 2017 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty
Keywords
- correlation functions
- fluctuation phenomena
- matrix models
- quantum chaos