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

Euler Equations of Motion01:19

Euler Equations of Motion

690
Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
690
Applications of Integration to Find Centers of Mass01:30

Applications of Integration to Find Centers of Mass

105
Rotational equilibrium provides a natural framework for defining the center of mass of a system. For a plank balanced on a pivot with two unequal masses, equilibrium is achieved when the net torque about the pivot is zero. Torque is defined as the product of a force and its perpendicular distance from the pivot. When the torques due to all forces cancel, the pivot coincides with the center of mass of the system.For a system composed of several discrete point masses, the center of mass lies at...
105
Rotation of Asymmetric Top01:11

Rotation of Asymmetric Top

1.7K
By definition, a spherically symmetric body has the same moment of inertia about any axis passing through its center of mass. This situation changes if there is no spherical symmetry. Since most rigid bodies are not spherically symmetric, these require special treatment.
The relationship between the angular momentum of any rigid body and its angular velocity, both of which are vectors, involves the moment of inertia. The moment of inertia is a scalar quantity only for spherically symmetric...
1.7K
Inertia Tensor01:24

Inertia Tensor

1.3K
The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least...
1.3K
Improper Integrals: Infinite Intervals01:29

Improper Integrals: Infinite Intervals

186
An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
186
Indefinite Integrals01:25

Indefinite Integrals

137
The water inflow rate into a storage tank is not constant but increases over time. Initially, the pump delivers water at a rate of 5 L/min. However, the inflow rate increases by 2 L/min for each additional minute due to rising pressure or system adjustments. This scenario can be described mathematically by a linear function:It is necessary to integrate the inflow rate function to measure the total volume of water added to the tank over time. The total water volume V(t) is obtained by performing...
137

You might also read

Related Articles

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

Sort by
Same author

Trotter transition in Bardeen-Cooper-Schrieffer pairing dynamics.

Physical review. E·2026
Same author

Partition function zeros of quantum many-body systems.

Physical review. E·2025
Same author

Instability of Metals with Respect to Strong Electron-Phonon Interaction.

Physical review letters·2025
Same author

Fundamental Limits on the Electron-Phonon Coupling and Superconducting T<sub>c</sub>.

Advanced materials (Deerfield Beach, Fla.)·2025
Same author

Yang-Lee zeros of certain antiferromagnetic models.

Physical review. E·2024
Same author

Dynamical chaos in the integrable Toda chain induced by time discretization.

Chaos (Woodbury, N.Y.)·2024
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Mar 19, 2026

2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

10.5K

Rotationally invariant ensembles of integrable matrices.

Emil A Yuzbashyan1, B Sriram Shastry2, Jasen A Scaramazza1

  • 1Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA.

Physical Review. E
|June 15, 2016
PubMed
Summary
This summary is machine-generated.

We introduce integrable matrix theory (IMT), a new framework for quantum integrable models. IMT generalizes random matrix theory (RMT) by constructing random integrable matrices with specified integrals.

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

9.8K
Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

10.6K

Related Experiment Videos

Last Updated: Mar 19, 2026

2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

10.5K
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

9.8K
Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

10.6K

Area of Science:

  • * Quantum mechanics
  • * Mathematical physics
  • * Statistical mechanics

Background:

  • * Random matrix theory (RMT) is a powerful tool for analyzing complex quantum systems.
  • * Quantum integrable models possess special properties that allow for exact solutions.
  • * Existing methods for studying integrable models lack a unified theoretical framework.

Purpose of the Study:

  • * To formulate integrable matrix theory (IMT) as a counterpart to RMT for quantum integrable models.
  • * To construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals.
  • * To develop a basis-independent formulation for these integrable matrices.

Main Methods:

  • * Definition of type-M families of integrable matrices, comprising N-M independent commuting N×N matrices.
  • * Development of a rotationally invariant parametrization for integrable matrices.
  • * Derivation of the joint probability density for integrable matrices.

Main Results:

  • * Construction of integrable matrix theory (IMT) for quantum integrable models.
  • * Establishment of a basis-independent formulation for integrable matrices.
  • * Derivation of the joint probability density for integrable matrices, analogous to Gaussian ensembles in RMT.

Conclusions:

  • * IMT provides a new theoretical framework for studying quantum integrable models.
  • * The developed methods allow for the analysis of random integrable matrices.
  • * This work bridges the gap between RMT and the study of integrable systems.