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 Concept Videos

Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

3.1K
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
3.1K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

46.3K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
46.3K
Aromatic Hydrocarbon Cations: Structural Overview01:18

Aromatic Hydrocarbon Cations: Structural Overview

3.0K
Cycloheptatriene is a neutral monocyclic unsaturated hydrocarbon that consists of an odd number of carbon atoms and an intervening sp3 carbon in the ring. The three double bonds in the ring correspond to 6 π electrons, which is a Huckel number, and therefore satisfies the criteria of 4n + 2 π electrons. However, the intervening sp3 carbon disrupts the continuous overlap of p orbitals. As a result, cycloheptatriene is not aromatic.
Removing one hydrogen from the intervening CH2 group...
3.0K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

8.1K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
8.1K
2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

925
Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
925
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

50.6K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
50.6K

You might also read

Related Articles

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

Sort by
Same author

Differences Between Robin and Neumann Eigenvalues.

Communications in mathematical physics·2021
Same author

Modelling the expected probability of correct assignment under uncertainty.

Scientific reports·2020
Same author

On probability measures arising from lattice points on circles.

Mathematische annalen·2020
See all related articles

Related Experiment Video

Updated: Sep 16, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.6K

On Quantum Ergodicity for Higher Dimensional Cat Maps.

Pär Kurlberg1, Alina Ostafe2, Zeev Rudnick3

  • 1Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden.

Communications in Mathematical Physics
|July 7, 2025
PubMed
Summary
This summary is machine-generated.

We show that eigenfunctions of higher dimensional cat maps become uniformly distributed for most quantum parameters. This extends previous results for two-dimensional systems, offering new insights into quantum chaos.

More Related Videos

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

9.1K
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

9.8K

Related Experiment Videos

Last Updated: Sep 16, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.6K
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

9.1K
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

9.8K

Area of Science:

  • Quantum chaos
  • Mathematical physics
  • Number theory

Background:

  • Cat maps are a model for quantum chaos, defined by linear symplectic maps.
  • Eigenfunction localization is a key phenomenon in quantum chaotic systems.
  • Previous work established uniform distribution for 2D cat maps.

Purpose of the Study:

  • To investigate eigenfunction localization in higher dimensional cat maps.
  • To extend the understanding of quantum chaos models beyond two dimensions.
  • To prove uniform distribution of eigenfunctions for a density one sequence of quantum parameters.

Main Methods:

  • Utilizing tools from additive combinatorics, including Bourgain's bound for Mordell sums.
  • Analyzing the tensor product structures specific to higher dimensional cat maps.
  • Developing new mathematical techniques to handle the increased complexity of higher dimensions.

Main Results:

  • Demonstrated uniform distribution of eigenfunctions for a density one sequence of integers N.
  • Showed that this result holds for higher dimensional cat maps (g > 1).
  • The methods employed differ significantly from those used for the 2D case.

Conclusions:

  • The study successfully extends results on eigenfunction distribution to higher dimensions.
  • New mathematical tools, particularly from additive combinatorics, are crucial for higher dimensional analysis.
  • This work deepens the understanding of quantum chaos in more complex systems.