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

Quantum Numbers02:43

Quantum Numbers

46.0K
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.
46.0K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

15.6K
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...
15.6K
Graphing the Wave Function01:13

Graphing the Wave Function

2.4K
Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
2.4K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

56.5K
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:
56.5K
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

1.3K
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...
1.3K
Graphs of Polar Equations01:17

Graphs of Polar Equations

38
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
38

You might also read

Related Articles

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

Sort by
Same author

Isoscattering non-isospectral quantum graphs.

Scientific reports·2025
Same author

Statistical analysis of level-spacing ratios in pseudointegrable systems: Semi-Poisson insight and beyond.

Physical review. E·2025
Same author

Spectral properties of chaotic microwave networks and quantum graphs under an edge swap transformation.

Physical review. E·2025
Same author

Coupled unidirectional chaotic microwave graphs.

Physical review. E·2024
Same author

Quantum graphs and microwave networks as narrow-band filters for quantum and microwave devices.

Physical review. E·2023
Same author

Experimental study of the elastic enhancement factor in a three-dimensional wave-chaotic microwave resonator exhibiting strongly overlapping resonances.

Physical review. E·2023

Related Experiment Video

Updated: Oct 26, 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

9.9K

A new spectral invariant for quantum graphs.

Michał Ławniczak1, Pavel Kurasov2, Szymon Bauch3

  • 1Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland. lawni@ifpan.edu.pl.

Scientific Reports
|July 29, 2021
PubMed
Summary
This summary is machine-generated.

A new spectral invariant, the generalized Euler characteristic, is introduced for quantum graphs and microwave networks. This invariant can be determined from low eigenfrequencies and helps identify Dirichlet vertices in physical systems.

More Related Videos

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

2.7K
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

871

Related Experiment Videos

Last Updated: Oct 26, 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

9.9K
ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

2.7K
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

871

Area of Science:

  • Graph theory
  • Spectral analysis
  • Mathematical physics

Background:

  • The Euler characteristic is a fundamental topological invariant for graphs.
  • Describing spectral properties of differential equations with mixed boundary conditions requires new invariants.
  • Quantum graphs and microwave networks are physical systems modeled by differential equations.

Purpose of the Study:

  • Introduce a new spectral invariant, the generalized Euler characteristic.
  • Demonstrate its theoretical and experimental determination from eigenfrequencies.
  • Establish its utility in identifying Dirichlet vertices and studying physical systems.

Main Methods:

  • Theoretical analysis of spectral properties.
  • Experimental determination using quantum graphs and microwave networks.
  • Analysis of lowest eigenfrequencies to extract the invariant.

Main Results:

  • The generalized Euler characteristic is defined and shown to be a spectral invariant.
  • It can be accurately determined from a small set of lowest eigenfrequencies.
  • The number of Dirichlet vertices can be deduced from the generalized Euler characteristic when graph topology is known.

Conclusions:

  • The generalized Euler characteristic is a powerful new tool for spectral analysis of graphs.
  • It enables the study of physical systems with mixed boundary conditions, such as isoscattering and neural networks.
  • This invariant provides a method to determine crucial topological information (Dirichlet vertices) from spectral data.