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

Nearest-neighbor distribution for singular billiards.

E Bogomolny1, O Giraud, C Schmit

  • 1Laboratoire de Physique Théorique et Modèles Statistiques, Université de Paris XI, Bâtiment 100, 91405 Orsay Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary
This summary is machine-generated.

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

[Chronic mesotympanic otitis media with an atypical course : A rare differential diagnosis].

HNO·2026
Same author

[Description and implementation of primary, secondary, and tertiary preventive strategies in otorhinolaryngology].

HNO·2026
Same author

Retrospective analysis of different application methods in intratympanic glucocorticoid therapy for treatment of idiopathic SSNHL: A comparative outcome study.

European archives of oto-rhino-laryngology : official journal of the European Federation of Oto-Rhino-Laryngological Societies (EUFOS) : affiliated with the German Society for Oto-Rhino-Laryngology - Head and Neck Surgery·2025
Same author

[Recurrent cholesteatoma after reconstruction of the auditory canal : Contradictory findings and differential diagnostic challenges].

HNO·2024
Same author

[Sudden-onset double vision-a complication requiring interdisciplinary treatment].

HNO·2024
Same author

Semiclassical evaluation of expectation values.

Physical review. E·2020
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

This study analyzes the nearest-neighbor spacing distribution in rectangular billiards with scatterers. Spectral statistics for these systems exhibit intermediate behavior, with level repulsion and exponential decay.

Area of Science:

  • Quantum chaos
  • Mathematical physics
  • Spectral statistics

Background:

  • Understanding spectral statistics in quantum systems is crucial for characterizing their behavior.
  • Billiard systems with internal scatterers provide a model for studying complex quantum dynamics.

Purpose of the Study:

  • To compute the nearest-neighbor spacing distribution P(s) for a rectangular billiard with a pointlike scatterer.
  • To investigate the asymptotic behavior of P(s) and the nth nearest-neighbor spacing distribution P(n)(s).
  • To classify the spectral statistics of such systems.

Main Methods:

  • Exact computation of the nearest-neighbor spacing distribution P(s).
  • Analysis of P(s) for periodic and Dirichlet boundary conditions.
  • Calculation of the nth nearest-neighbor spacing distribution P(n)(s) for arbitrary boundary conditions.

Related Experiment Videos

Main Results:

  • The nearest-neighbor spacing distribution P(s) decreases exponentially as s approaches infinity.
  • The spectral statistics are of an intermediate type, showing level repulsion at small distances and exponential decay at large distances.
  • Asymptotic behavior of P(n)(s) was determined for all boundary conditions.

Conclusions:

  • The spectral statistics of rectangular billiards with pointlike scatterers are confirmed to be of an intermediate type.
  • The exponential decay of P(s) at large distances is a key characteristic of these systems.
  • The study provides a comprehensive analysis of nearest-neighbor spacing distributions in such quantum systems.