Accuracy of Trace Formulas

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.

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

References in corpus (1)

• On the Quantum Baker's Map and its Unusual Traces

Cited by in corpus (10)

• Entanglement between two subsystems, the Wigner semicircle and extreme value statistics
• Recurrence of fidelity in near integrable systems
• Generalized Gaussian wave packet dynamics: Integrable and Chaotic Systems
• Classical Diffusion and Quantum Level Velocities: Systematic Deviations from Random Matrix Theory
• Phase space localization of chaotic eigenstates: Violating ergodicity
• Controlling Quantum Chaos: Optimal Coherent Targeting
• Exploring classical phase space structures of nearly integrable and mixed quantum systems via parametric variation
• Periodic orbit quantization of a Hamiltonian map on the sphere
• A semiclassical reversibility paradox in simple chaotic systems
• Level velocity statistics of hyperbolic chaos