What is quantum chaos?
(Thanks to Leon Poon for contributing to this answer) According to the correspondence principle, there is a limit where classical behavior as described by Hamilton’s equations becomes similar, in some suitable sense, to quantum behavior as described by the appropriate wave equation. Formally, one can take this limit to be h -> 0, where h is Planck’s constant; alternatively, one can look at successively higher energy levels. Such limits are referred to as “semiclassical”. It has been found that the semiclassical limit can be highly nontrivial when the classical problem is chaotic. The study of how quantum systems, whose classical counterparts are chaotic, behave in the semiclassical limit has been called quantum chaos. More generally, these considerations also apply to elliptic partial differential equations that are physically unrelated to quantum considerations. For example, the same questions arise in relating classical waves to their corresponding ray equations. Among recent results
