Hierarchical Structure in the Trace Formula
Jonathan P. Keating
TL;DR
This paper reveals a hierarchical structure in Guztwiller's Trace Formula, linking periodic orbit contributions to spectral statistics in quantum chaos, with implications for spectral determinants and connections to Random Matrix Theory and Number Theory.
Contribution
It uncovers a new hierarchical organization in the Trace Formula, enhancing understanding of spectral statistics in quantum chaotic systems.
Findings
Identifies a hierarchical pattern in orbit contributions
Links spectral determinants to Random Matrix Theory
Provides insights into quantum chaos spectral statistics
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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