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 Experiment Video

Updated: Jun 7, 2025

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings
09:01

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings

Published on: April 16, 2017

7.7K

Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.

László Erdős1, Volodymyr Riabov1

  • 1Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.

Communications in Mathematical Physics
|November 11, 2024
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

Thermal Sigmatropic Reactions: Overview01:16

Thermal Sigmatropic Reactions: Overview

2.1K
Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in...
2.1K
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

950
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
950
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

630
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
630
Entropy02:39

Entropy

28.8K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
28.8K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

879
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
879
Thermal Strain01:19

Thermal Strain

673
Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
673

You might also read

Related Articles

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

Sort by
Same author

Linear Eigenvalue Statistics at the cusp.

Probability theory and related fields·2025
Same author

Cusp Universality for Correlated Random Matrices.

Communications in mathematical physics·2025
Same author

On the Spectral Form Factor for Random Matrices.

Communications in mathematical physics·2023
Same author

Edge universality for non-Hermitian random matrices.

Probability theory and related fields·2021
Same author

Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.

Communications in mathematical physics·2020
Same journal

A Mathematical Analysis of IPT-DMFT.

Communications in mathematical physics·2026
Same journal

Asymptotics of Symmetric Polynomials: A Dynamical Point of View.

Communications in mathematical physics·2026
Same journal

Commuting Quantum Operations Factorise.

Communications in mathematical physics·2026
Same journal

On the Open TS/ST Correspondence.

Communications in mathematical physics·2026
Same journal

A Superintegrable Quantum Field Theory.

Communications in mathematical physics·2026
Same journal

High-Contrast Random Composites: Homogenisation Framework and Spectral Convergence.

Communications in mathematical physics·2026
See all related articles

We prove the Eigenstate Thermalization Hypothesis for Wigner-type matrices, demonstrating its robustness across diverse random matrix ensembles. This confirms thermalization in quantum systems with complex structures, even with vanishing entries.

Area of Science:

  • Quantum mechanics
  • Random matrix theory
  • Statistical physics

Background:

  • The Eigenstate Thermalization Hypothesis (ETH) is a cornerstone in understanding how isolated quantum systems reach thermal equilibrium.
  • Previous studies often focused on specific random matrix ensembles or simpler systems, leaving broader applicability uncertain.
  • Investigating ETH in Wigner-type matrices is crucial for understanding thermalization in complex quantum systems.

Purpose of the Study:

  • To rigorously prove the Eigenstate Thermalization Hypothesis for a general class of Wigner-type random matrices.
  • To establish optimal control over fluctuations for observables of arbitrary rank within the bulk spectrum.
  • To demonstrate the robustness of ETH under very general conditions, including those with vanishing matrix entries.

Main Methods:

More Related Videos

Characterization of Thermal Transport in One-dimensional Solid Materials
05:20

Characterization of Thermal Transport in One-dimensional Solid Materials

Published on: January 26, 2014

17.3K
Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere
08:52

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Published on: April 30, 2018

8.1K

Related Experiment Videos

Last Updated: Jun 7, 2025

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings
09:01

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings

Published on: April 16, 2017

7.7K
Characterization of Thermal Transport in One-dimensional Solid Materials
05:20

Characterization of Thermal Transport in One-dimensional Solid Materials

Published on: January 26, 2014

17.3K
Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere
08:52

Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere

Published on: April 30, 2018

8.1K
  • Development and application of rank-uniform optimal local laws for one and two resolvents of Wigner-type matrices.
  • Analysis of observables with regular properties.
  • Consideration of diverse variance profiles, including those with many vanishing entries.

Main Results:

  • Rigorous proof of the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the spectral bulk.
  • Optimal control on fluctuations for arbitrary rank observables is achieved.
  • Demonstration that ETH holds robustly across a diverse class of random matrix ensembles.

Conclusions:

  • The Eigenstate Thermalization Hypothesis is proven to be a robust phenomenon for Wigner-type matrices.
  • The findings confirm ETH's validity in quantum systems with non-trivial spatial structures and under general conditions.
  • This work provides a significant theoretical advancement in understanding thermalization in complex quantum systems.