Periodic orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit

• URL: http://arxiv.org/abs/2101.00006v3
• Date: Tue, 29 Mar 2022 17:20:30 GMT
• Title: Periodic orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit
• Authors: Jon Harrison and Tori Hudgins
• Abstract summary: We evaluate a spectral statistic of chaotic 4-regular quantum graphs from their periodic orbits without the semiclassical limit. We observe the mechanism that connects semiclassical results to the total number of orbits regardless of their structure.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Energy level statistics of quantized chaotic systems have been evaluated in the semiclassical limit via their periodic orbits using the Gutzwiller and related trace formulae. Here we evaluate a spectral statistic of chaotic 4-regular quantum graphs from their periodic orbits without the semiclassical limit. The variance of the n-th coefficient of the characteristic polynomial is determined by the sizes of the sets of distinct primitive periodic orbits with n bonds which have no self-intersections, and the sizes of the sets with a given number of self-intersections which all consist of two sections of the pseudo orbit crossing at a single vertex. Using this result we observe the mechanism that connects semiclassical results to the total number of orbits regardless of their structure.

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