Hierarchical Structure in the Trace Formula
- URL: http://arxiv.org/abs/2205.13815v1
- Date: Fri, 27 May 2022 08:06:35 GMT
- Title: Hierarchical Structure in the Trace Formula
- Abstract summary: Guztwiller's Trace Formula is central to the semiclassical theory of quantum energy levels and spectral statistics in classically chaotic systems.
Motivated by recent developments in Random Matrix Theory and Number Theory, we elucidate a hierarchical structure in the way periodic orbits contribute to the Trace Formula.
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- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Guztwiller's Trace Formula is central to the semiclassical theory of quantum
energy levels and spectral statistics in classically chaotic systems. Motivated
by recent developments in Random Matrix Theory and Number Theory, we elucidate
a hierarchical structure in the way periodic orbits contribute to the Trace
Formula that has implications for the value distribution of spectral
determinants in quantum chaotic systems.
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