Quantization ambiguity, ergodicity and semiclassics
Quantization ambiguity, ergodicity and semiclassics
A simple argument shows that eigenstates of a classically ergodic system are individually ergodic on coarse-grained scales. This has implications for the quantization ambiguity in ergodic systems: the difference between alternative quantizations is suppressed compared with the $O(\hbar^2)$ ambiguity in the integrable case. For two-dimensional ergodic systems in the high-energy …