Accuracy of Trace Formulas
chao-dyn
2009-10-28 v1 Chaotic Dynamics
Quantum Physics
Abstract
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.
Cite
@article{arxiv.chao-dyn/9606005,
title = {Accuracy of Trace Formulas},
author = {Arul Lakshminarayan},
journal= {arXiv preprint arXiv:chao-dyn/9606005},
year = {2009}
}
Comments
20 pages, uuencoded and gzipped, 1 LaTex text file and 9 PS files for figures