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Universal spectral correlations from the ballistic sigma model.

Jan Müller¹, Tobias Micklitz, Alexander Altland

¹Institut für Theoretische Physik, Zülpicher Str 77, 50937 Köln, Germany.

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

|February 1, 2008

Summary

This study uses the semiclassical ballistic sigma model to explain quantum interference in chaotic systems. It reveals how periodic orbits in quantum mechanics relate to universal behaviors predicted by random matrix theory.

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Area of Science:

Quantum mechanics
Statistical physics
Chaos theory

Background:

Classically chaotic systems exhibit complex quantum mechanical behavior.
Understanding quantum interference in these systems is crucial.
Random matrix theory (RMT) describes universal properties of chaotic systems.

Purpose of the Study:

To apply the semiclassical ballistic sigma model to chaotic quantum systems.
To explore analogies between this model and semiclassical theories of quantum interference.
To provide a field-theoretic understanding of universality in chaotic systems.

Main Methods:

Utilizing the semiclassical ballistic sigma model as an effective field theory.
Analyzing semiclassical "diagrams" representing periodic orbits.
Connecting field theory descriptions to quantum interference phenomena.

Main Results:

Demonstrated emergence of semiclassical diagrams from the field theory.
Established a link between periodic orbits and quantum interference.
Provided a field-theoretic explanation for RMT universality in chaotic systems.

Conclusions:

The semiclassical ballistic sigma model offers a powerful framework for studying quantum chaos.
Periodic orbits play a key role in understanding quantum interference and universality.
Field theory provides insights into the fundamental nature of chaotic quantum systems.