Applications of Chinese remainder theorem to physics?

Question

I'm teaching algebra to a physicist. The next thing I'm going to introduce is the Chinese remainder theorem, including the Chinese remainder theorem for principal ideal domains, and later possibly for modules. I want to find some application of it to physics, but, although having been trained as a (theoretical) physicist myself, and having googled a fair bit, I wasn't able to find any (apart from range ambiguity resolution for radars, but that doesn't really count as physics, it's an algorithm). So, I ask if anyone knows applications of the Chinese remainder theorem to (possibly, mathematical) physics per se. Just in case, I consider quantum computation theory a part of physics.

Answer 1

One should note that the Chinese Remainder Theorem is so useful in its own right, and interesting in its own right, that one should not need to find an application to physics in order to motivate its discussion. A person who is interested in physics should be interested in a wide enough variety of topics that some other application could be accepted.

However, in computational physics, there is an important use-case that however is not fundamental. When we want to work with crystalline physics, there is often the need to consider supercells, so that the most simple Brillouin zone is folded one way or another. When we want to map data from one supercell to another supercell that is incongruent, i.e. not a multiple of the first one, then the unfolding and refolding process is very much helped by knowing details related to the Chinese Remainder Theorem.

I am sure that there are other applications. Like, there are definitely many discretisations of stuff that ostensibly should have circular symmetry, and once discretised, they would fall under the purview of Chinese Remainder Theorem. It is just that I can quickly think of this application from memory.