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

Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

12.7K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
12.7K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.1K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.1K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

805
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
805
Quantum Numbers02:43

Quantum Numbers

35.1K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
35.1K
Aliasing01:18

Aliasing

189
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
189
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

1.1K
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
1.1K

You might also read

Related Articles

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

Sort by
Same author

Guiding waves through chaos: Universal bounds for targeted mode transport.

Science advances·2026
Same author

Microwave experiments in the realm of fidelity.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2016
See all related articles

Related Experiment Video

Updated: Aug 13, 2025

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

9.7K

Implications of Spectral Interlacing for Quantum Graphs.

Junjie Lu1, Tobias Hofmann2, Ulrich Kuhl1,2

  • 1Institut de Physique de Nice, CNRS, Université Côte d'Azur, 06108 Nice, France.

Entropy (Basel, Switzerland)
|January 21, 2023
PubMed
Summary
This summary is machine-generated.

Quantum graphs reveal spectral statistics of chaotic systems. Dirichlet graphs offer analytic expressions for level spacing and number variance, while Neumann graphs show deviations from random matrix predictions.

Keywords:
interlacing theoremquantum graphsrandom matrix theory

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
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.6K

Related Experiment Videos

Last Updated: Aug 13, 2025

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

9.7K
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
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.6K

Area of Science:

  • Quantum physics
  • Spectral statistics
  • Chaos theory

Background:

  • Quantum graphs are models for chaotic systems.
  • Neumann and Dirichlet boundary conditions yield different spectral properties.
  • Neumann eigenvalues deviate from random matrix predictions due to interlacing theorems.

Purpose of the Study:

  • Derive analytic expressions for Dirichlet graphs.
  • Compare analytic and numerical results for Dirichlet graphs.
  • Analyze spectral statistics of small Neumann graphs.

Main Methods:

  • Ensemble averaging of spectra.
  • Derivation of analytic expressions for level spacing and number variance.
  • Numerical simulations for Dirichlet and Neumann graphs.

Main Results:

  • Analytic expressions for Dirichlet graphs' spectral statistics presented.
  • Numerical results confirm analytic predictions for Dirichlet graphs.
  • Deviations from random matrix predictions observed for Neumann graphs.

Conclusions:

  • Dirichlet graphs provide a framework for understanding spectral statistics.
  • Neumann graphs exhibit distinct statistical behaviors compared to random matrix theory.
  • The bond number influences spectral statistics in quantum graphs.