Trace identities and their semiclassical implications

Details Trace identities and their semiclassical implications Trace identities and their semiclassical implications

1999-09-07

arxiv.org/abs/chao-dyn/9909011v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

LaTeX - IOP style

Scientific paper

10.1088/0305-4470/33/11/310

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically {\it integrable} maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The same technique is not applicable for {\it chaotic} maps, and the compatibility of the semiclassical theory in this case remains unsettled. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions.

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