|
| related topics |
| {classical, space, random} |
| {phase, path, phys} |
| {energy, state, states} |
| {equation, function, exp} |
| {theory, mechanics, state} |
| {energy, gaussian, time} |
| {field, particle, equation} |
| {cos, sin, state} |
| {operator, operators, space} |
| {information, entropy, channel} |
|
Quantization Ambiguity, Ergodicity, and Semiclassics
L. Kaplan
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 $O(\hbar^2)$ 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 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9906065
- categories:
- quant-ph chao-dyn nlin.CD
- comments:
- 4 pages, with 2 figures
- doi:
- 10.1088/1367-2630/4/1/390
- arxiv_id:
- quant-ph/9906065
- journal_ref:
- New J.Phys. 4 (2002) 90
- created:
- 1999-06-17
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