Higher Dimensional Fourier Quasicrystals from Lee-Yang Varieties

Abstract

In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions in ${\mathbb{C}}^n$, which generalize hypersurfaces defined by Lee-Yang polynomials. We show that these are Delone almost periodic sets that have at most finite intersection with every discrete periodic set.

References in corpus (12)

• Hyperuniform States of Matter
• Quasicrystals and Poisson's summation formula
• Sign variation, the Grassmannian, and total positivity
• Fourier quasicrystals and discreteness of the diffraction spectrum
• Stable polynomials and crystalline measures
• Network Parameterizations for the Grassmannian
• Livsic-type Determinantal Representations and Hyperbolicity
• Decompositions of amplituhedra
• Real Fibered Morphisms and Ulrich Sheaves
• The separating semigroup of a real curve
• The Chow form of a reciprocal linear space
• Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial