Year: 2026
Type: preprint
Abstract: We prove that Fourier quasicrystal measures with positive integer masses are precisely the nonzero real sections of effective Lee-Yang cycles by matrices with positive maximal minors, with masses given by weighted local intersection degrees. For Delone support, the reduced support of the cycle can be chosen strict. For unit masses, the cycle can be chosen reduced, with local intersection degree one at every root. Every integer-mass FQ measure has support equal to the common complex zero set of finitely many real-valued trigonometric polynomials. These results answer Questions (1), (2), and (4) of Alon, Kummer, Kurasov, and Vinzant. We recover a finite-dimensional torus from the spectrum and prove that its canonical analytic set is algebraic. A support-height theorem for holonomic sequences provides a linear spectral bound, from which we reconstruct the complex branches and their integer coefficients using fiber moments. Singular sections carry their natural local intersection degrees; discarding these can destroy the Fourier quasicrystal property.
Source: arXiv (Cornell University)
Author: Wei, Dongsheng
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221131029