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Related Experiment Video

Updated: May 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Chaotic scattering on individual quantum graphs.

Z Pluhař¹, H A Weidenmüller

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 17, 2013

Summary

The semiclassical approximation is exact for chaotic scattering on quantum graphs. Researchers used supersymmetry and other methods to calculate exact correlation functions, confirming results from random-matrix theory.

Related Experiment Videos

Last Updated: May 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum mechanics
Chaos theory
Mathematical physics

Background:

The semiclassical approximation is often used in quantum mechanics.
Chaotic scattering on quantum graphs presents unique theoretical challenges.
Understanding correlation functions is key to characterizing chaotic systems.

Purpose of the Study:

To calculate exact expressions for correlation functions of the scattering matrix in quantum chaotic scattering.
To investigate the validity of the semiclassical approximation in this regime.
To compare results with established random-matrix theory approaches.

Main Methods:

Utilizing the exactness of the semiclassical approximation for quantum graphs.
Employing advanced techniques: supersymmetry, color-flavor transformation, and saddle-point approximation.
Calculating lowest and asymptotic expressions for higher correlation functions.

Main Results:

Derived exact expressions for all higher correlation functions of the scattering matrix.
Confirmed agreement between the novel approach and random-matrix theory predictions.
Established the Ericson regime's relevance for asymptotic expressions.

Conclusions:

The employed methods provide exact results for quantum chaotic scattering correlation functions.
The findings support the universality of these results in quantum-chaotic scattering.
This work bridges semiclassical and random-matrix theories for chaotic systems.