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Very interesting question. Perhaps by looking at fuzziness in the spectral lines of elements in asteroids (which are sometimes composed of quasicrystals [0]).

Looks like there has been some work on NMR of quasicrystals [1].

Zeeman splitting of spectral lines requires a magnetic field. Maybe if a large quasicrystal passed near a magnetar [3] one would see an effect.

[0]: https://www.pnas.org/content/113/26/7077 [1]: https://link.springer.com/article/10.1007/BF03166327 [2]: http://adsabs.harvard.edu/full/1990ApJS...74..437S [3]: https://en.m.wikipedia.org/wiki/Magnetar



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