Quantization Ambiguity, Ergodicity, and Semiclassics

Abstract

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 $O({\hslash }^2)$ 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 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.

4 pages, with 2 figures

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Cited by in corpus (5)

• Dynamics of Loschmidt echoes and fidelity decay
• A random matrix formulation of fidelity decay
• Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions
• Semiclassical Accuracy in Phase Space for Regular and Chaotic Dynamics
• Mode resolved travel time statistics for elastic rays in three-dimensional billiards