Friday, 5 June 2020

classical mechanics - Is there a physical system whose phase space is the torus?


NOTE. This is not a question about mathematics and in particular it's not a question about whether one can endow the torus with a symplectic structure.


In an answer to the question


What kind of manifold can be the phase space of a Hamiltonian system?


I claimed that there exist (in a mathematical sense), Hamiltonian systems on the torus (and in fact on higher genus surfaces as well). However, when pressed to come up with a physical system in the real world (even an idealized one) whose dynamics could be modeled as a Hamiltonian system on the torus, I could not think of one.


Does such a system exist?


I would even be satisfied with a non-classical system which can somehow effectively be described by a Hamiltonian system on the torus, although I'm not sure that the OP of the other question I linked to above would be.




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