Controlled long-time classical limits

The classical limit asks how and when Newtonian/Hamiltonian mechanics emerges from quantum dynamics as $\hbar\to0$ or for macroscopic systems. It is subtle because the limit is singular and, for chaotic systems, quantum and classical predictions diverge after a surprisingly short time.

What is known: Egorov-type results control semiclassical observable evolution under stated smoothness and time assumptions; coherent-state and mean-field limits also have rigorous regimes. In chaotic dynamics, derivative growth often limits naive wave-packet or operator estimates to logarithmic Ehrenfest times. This is not a universal prohibition on every coarse observable having longer correspondence, nor a theorem that decoherence is always necessary.

Selected child questions ask for errors beyond established Ehrenfest windows for specified coarse observables; for joint noise/semiclassical limits with quantified decoherence; and for macroscopic mean-field or hydrodynamic limits with size-dependent times. State the metric, initial-state class and order of limits. These distinct tasks cannot be certified by a blanket claim of a universal classical-limit theorem. Related: F5, M8 (quantum unique ergodicity), M9 (spectral statistics), B5 (thermalization).

Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.