Missing-level statistics in classically chaotic quantum systems with symplectic symmetry

TL;DR

This paper investigates the fluctuation properties of incomplete spectra in quantum systems with symplectic symmetry, validating extended random-matrix theory predictions through experiments and numerical simulations, and demonstrating the ability to identify missing levels and symmetry class.

Contribution

The authors extend RMT predictions for incomplete spectra to systems with symplectic symmetry and validate these predictions experimentally and numerically, enabling identification of missing levels and symmetry classification.

Findings

RMT predictions match experimental and numerical incomplete spectra

It is possible to determine the fraction of missing levels from fluctuation analysis

Symmetry class can be identified by comparing fluctuation properties with RMT

Abstract

We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend the random-matrix theory (RMT) approach introduced in [O. Bohigas and M. P. Pato, Phys. Rev. E 74, 036212 (2006)] for incomplete spectra of quantum systems with orthogonal symmetry. We validate these RMT predictions by randomly extracting a fraction of levels from complete sequences obtained numerically for quantum graphs and experimentally for microwave networks with symplectic symmetry and then apply them to incomplete experimental spectra to demonstrate their applicability. Independently of their symmetry class quantum graphs exhibit nongeneric features which originate from nonuniversal contributions. Part of the associated eigenfrequencies can be identified in the level dynamics of parameter-dependent quantum graphs and extracted, thereby yielding spectra with systematically missing eigenfrequencies. We demonstrate that, even though the RMT approach relies on the assumption that levels are missing at random, it is possible to determine the fraction of missing levels and assign the appropriate symmetry class by comparison of their fluctuation properties with the RMT predictions.