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

Atomic Spectroscopy: Effects of Temperature01:27

Atomic Spectroscopy: Effects of Temperature

540
Atomization, converting samples into gas-phase atoms and ions, is essential for atomic spectroscopy. The flame temperature required for atomization affects the efficiency of the atomic spectroscopic methods by increasing the atomization efficiency and the relative population of the excited and ground states.
At thermal equilibrium, the relative populations of excited and ground state atoms can be estimated using the Maxwell–Boltzmann distribution. For example, an increase in temperature...
540
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

1.4K
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.
1.4K
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

449
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
449
Fermi Level Dynamics01:12

Fermi Level Dynamics

382
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
382
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.2K
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...
1.2K
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

771
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.
771

You might also read

Related Articles

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

Sort by
Same author

Eigenstate Thermalization Hypothesis Correlations via Nonlinear Hydrodynamics.

Physical review letters·2026
Same author

Steady-state heat engines driven by finite reservoirs.

Physical review. E·2026
Same author

Emergence of Generic Entanglement Structure in Doped Matchgate Circuits.

Physical review letters·2026
Same author

Entropic Costs of Extracting Classical Ticks from a Quantum Clock.

Physical review letters·2025
Same author

Information geometry of transitions between quantum nonequilibrium steady states.

Physical review. E·2025
Same author

Enhancing Revivals via Projective Measurements in a Quantum Scarred System.

Physical review letters·2025

Related Experiment Video

Updated: Oct 16, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

8.7K

Out-of-time-order correlations and the fine structure of eigenstate thermalization.

Marlon Brenes1, Silvia Pappalardi2, Mark T Mitchison1

  • 1Department of Physics, Trinity College Dublin, Dublin 2, Ireland.

Physical Review. E
|October 16, 2021
PubMed
Summary

Out-of-time-order correlators (OTOCs) precisely probe the Eigenstate Thermalization Hypothesis (ETH) by revealing correlations beyond standard predictions. Long-time OTOC behavior indicates an energy scale linked to random matrix theory, offering insights into quantum thermalization.

More Related Videos

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.6K
Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research
08:12

Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research

Published on: February 16, 2024

12.3K

Related Experiment Videos

Last Updated: Oct 16, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

8.7K
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

7.6K
Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research
08:12

Author Spotlight: Exploring Light-Driven Chemical Reactions and Energy-Harnessing Devices in Photochemical Research

Published on: February 16, 2024

12.3K

Area of Science:

  • Quantum Many-Body Physics
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • Out-of-time-order correlators (OTOCs) are crucial for understanding quantum information scrambling and thermalization in complex systems.
  • Recent theories suggest OTOCs reveal correlations beyond the standard Eigenstate Thermalization Hypothesis (ETH).

Purpose of the Study:

  • To explicitly demonstrate how OTOCs serve as precise tools for exploring the detailed structure of the ETH.
  • To investigate the connection between OTOC dynamics and underlying quantum correlations.

Main Methods:

  • Extensive numerical analysis of operator matrix element statistics.
  • Detailed study of OTOC dynamics across different timescales.
  • Investigation of finite-size scaling for an operator-dependent energy scale.

Main Results:

  • Short-time OTOC dynamics are primarily influenced by correlations.
  • Long-time OTOC saturation reveals an operator-dependent energy scale (ω_{GOE}), signaling the onset of an effective Gaussian random matrix theory.
  • A linear finite-size scaling of ω_{GOE} was observed for sums of local operators in the infinite-temperature regime.

Conclusions:

  • OTOCs are powerful probes for the fine details of the ETH, going beyond standard predictions.
  • The emergence of an effective Gaussian random matrix theory, characterized by ω_{GOE}, is a key feature of long-time thermalization dynamics.