John Carlos Baez on Nostr: HYPERUNIFORM MATTER I love weird states of matter, and here's another. Atoms of gas ...

HYPERUNIFORM MATTER

I love weird states of matter, and here's another.

Atoms of gas look like the dots at left. But if you ask people to draw dots as randomly as possible, they often draw something like the dots at right. Their dots are more uniformly distributed!

People are starting to find and study 'hyperuniform' materials, where randomness at large distance scales is suppressed - as in the picture at right. In a crystal randomness is highly suppressed, so technically crystals are hyperuniform, but that's boring.

The pattern you get when you take a bunch of balls and pack them tightly but randomly is hyperuniform - they're called 'jammed packed spheres'. So are the veins of many leaves! And so a quasicrystal, like a Penrose tiling, where there's a systematic pattern that doesn't ever quite repeat itself.

In a gas, the atoms obey a 'Poisson distribution', and one thing this implies is that the variance of the number of atoms in some region is proportional to the volume of that region - or in 2 dimensions, the area. The technical definition of hyperuniformity is that the variance of the number of atoms in some region grows more slowly than the volume for large volumes.

In case you're wondering: the atoms in water don't obey a Poisson distribution: they display patterns at short distances. But they're not hyperuniform because these patterns quickly go away at larger distances.

For more, check out this:

• Wikipedia, Hyperuniformity, https://en.wikipedia.org/wiki/Hyperuniformity

and this:

• Salvatore Torquato, Hyperuniform states of matter, https://arxiv.org/abs/1801.06924.