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Related Experiment Video

Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum chaos in one dimension?

László Ujfalusi1, Imre Varga, Dániel Schumayer

  • 1Elméleti Fizika Tanszék, Fizikai Intézet, Budapesti Műszaki és Gazdaságtudományi Egyetem, Budapest, Hungary.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 27, 2011
PubMed
Summary

Researchers inverted the Bohigas-Giannoni-Schmit conjecture, finding a one-dimensional potential with random matrix eigenvalue statistics. The resulting potential is nowhere differentiable or continuous in the limit of many eigenvalues.

Related Experiment Videos

Last Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Quantum mechanics
  • Mathematical physics

Background:

  • The Bohigas-Giannoni-Schmit conjecture relates quantum chaos to random matrix theory.
  • Investigating the inverse problem seeks potentials that exhibit specific spectral properties.

Purpose of the Study:

  • To explore the inverse of the Bohigas-Giannoni-Schmit conjecture.
  • To compute a one-dimensional potential whose eigenvalues follow random matrix statistics.

Main Methods:

  • Employed two distinct inversion techniques.
  • Analyzed the spectral properties of the computed potential.

Main Results:

  • Successfully computed a one-dimensional potential exhibiting random matrix eigenvalue statistics.
  • Numerical results show the potential is nowhere differentiable and likely nowhere continuous as N approaches infinity.

Conclusions:

  • The study suggests that a counterexample to the conjecture, in its inverse form, does not exist.
  • The computed potential serves as a significant finding in the study of quantum chaos and spectral properties.