Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Chaotic scattering on graphs

Kottos1, Smilansky

  • 1Max-Planck-Institut fur Stromungsforschung, 37073 Gottingen, Germany.

Physical Review Letters
|September 16, 2000
PubMed
Summary
This summary is machine-generated.

Quantized, compact graphs connected to infinite leads exhibit quantum chaotic scattering. This study provides exact formulas for scattering matrices and resonance densities, validating with random matrix theory predictions.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Quantum-mechanical nonperturbative response of driven chaotic mesoscopic systems

Physical review letters·2000
Same author

Statistics of resonances and of delay times in quasiperiodic Schrodinger equations

Physical review letters·2000
Same author

Wave packet dynamics in energy space, random matrix theory, and the quantum-classical correspondence

Physical review letters·2000
Same author

Periodic-orbit theory of anderson localization on graphs

Physical review letters·2000
Same author

Scaling properties of Lyapunov spectra for the band random matrix model.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·1996
Same author

Penumbra diffraction in the quantization of dispersing billiards.

Physical review letters·1996
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Chaos theory

Background:

  • Quantized, compact graphs model bounded quantum systems.
  • Understanding quantum chaos in scattering is crucial.

Purpose of the Study:

  • To demonstrate quantum chaotic scattering in connected graph systems.
  • To derive exact semiclassical expressions for scattering properties.

Main Methods:

  • Connecting quantized, compact graphs to infinite leads.
  • Deriving exact expressions for the scattering matrix.
  • Developing an exact trace formula for resonance density.

Main Results:

  • The system exhibits features of quantum chaotic scattering.

Related Experiment Videos

  • Exact formulas analogous to semiclassical theory were derived.
  • Statistical analysis aligns with random matrix theory predictions.

    • Conclusions:

    • Connected quantized graphs serve as a model for quantum chaotic scattering.
    • This system facilitates the study of generic chaotic scattering behavior.
    • It offers a tool for exploring semiclassical descriptions of quantum chaos.