Characterize the spacetime hyperuniformity of the 3+1-dimensional quasicrystal

Test whether the three-plus-one-dimensional spacetime quasicrystal is spacetime hyperuniform, extending the established result for the one-plus-one-dimensional construction.

Background

The thesis develops a spacetime generalization of hyperuniformity and shows that the one-plus-one-dimensional quasicrystal constructed from the I_{3,1} lattice is spacetime hyperuniform. It also presents numerical evidence that spacetime quasicrystals may outperform Poisson sprinklings in the number-volume correspondence.

The corresponding hyperuniformity status of the three-plus-one-dimensional quasicrystal remains untested in the stated summary.

References

Finally, we attempt to understand these results by extending the concept of hyperuniformity from space to spacetime, and we show that our $(1+1)$D quasicrystal is the first structure shown to be indeed spacetime hyperuniform (we leave testing the $(3+1)$D quasicrystal for a future work).

— Spacetime Quasicrystals and Computational Complexity Theory in the Road Towards Quantum Gravity  (2610.09855 - Mygdalas, 7 Oct 2026) in Abstract, Part II: Spacetime Quasicrystals