Accuracy of Trace Formulas

Details Accuracy of Trace Formulas Accuracy of Trace Formulas

1996-06-14

arxiv.org/abs/chao-dyn/9606005v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, uuencoded and gzipped, 1 LaTex text file and 9 PS files for figures

Scientific paper

10.1007/BF02845660

Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence of fixed points on singularities the trace formula may be exact, and in any case has no logarithmic divergences observed for the quantum bakers map. As a byproduct we introduce fantastic periodic curves akin to curlicues.

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