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Related Experiment Video

Updated: Apr 30, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Universal quantum graphs.

Z Pluhař¹, H A Weidenmüller²

¹Faculty of Mathematics and Physics, Charles University, 180 00 Praha 8, Czech Republic.

Physical Review Letters

|April 29, 2014

Summary

We proved the Bohigas-Giannoni-Schmit conjecture for time-reversal invariant graphs. Spectral correlations in mixing graphs match random matrix theory, and S-matrix correlations are derived for open graphs.

Area of Science:

Quantum Chaos
Statistical Mechanics
Random Matrix Theory

Background:

The Bohigas-Giannoni-Schmit conjecture relates spectral properties of quantum systems to random matrix theory.
Understanding spectral correlations is key to characterizing quantum chaotic systems.

Purpose of the Study:

To prove the Bohigas-Giannoni-Schmit conjecture in its most general form.
To extend these findings to open quantum systems and S-matrix correlations.

Main Methods:

Analysis of time-reversal invariant graphs.
Investigation of spectral correlation functions in the classical limit.
Derivation of S-matrix correlation functions for open graphs.

Main Results:

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Proved the conjecture for mixing, time-reversal invariant graphs, showing spectral correlations match the Gaussian Orthogonal Ensemble.
Derived analogous identities for S-matrix correlation functions in open graphs.

Conclusions:

The study confirms a fundamental link between quantum chaos and random matrix theory for closed systems.
It extends this connection to open systems, providing new tools for analyzing complex quantum dynamics.