Quantization ambiguity, ergodicity and semiclassics

Lev Kaplan
2002 New Journal of Physics  
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 regime, individual eigenstates are independent of the choice of quantization procedure, in contrast with the regular
more » ... with the regular case, where even the ordering of eigenlevels is ambiguous. Surprisingly, semiclassical methods are shown to be much more precise for chaotic than for integrable systems.
doi:10.1088/1367-2630/4/1/390 fatcat:ndl652b7hff37n4prioczpfsce