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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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 one, the...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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.
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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. This...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...

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Related Experiment Video

Updated: May 14, 2026

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

Eigenstate thermalization within isolated spin-chain systems.

R Steinigeweg1, J Herbrych, P Prelovšek

  • 1J. Stefan Institute, SI-1000 Ljubljana, Slovenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 16, 2013
PubMed
Summary
This summary is machine-generated.

Isolated spin chains exhibit distinct thermalization behaviors. Integrable systems deviate from the eigenstate thermalization hypothesis, unlike nonintegrable ones, showing similarities to noninteracting fermions.

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Last Updated: May 14, 2026

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

  • Quantum statistical mechanics
  • Condensed matter physics
  • Many-body systems

Background:

  • Understanding thermalization in isolated quantum systems is crucial for statistical mechanics.
  • The eigenstate thermalization hypothesis (ETH) describes thermalization in generic nonintegrable systems.
  • Integrable systems often exhibit unique behaviors deviating from ETH.

Purpose of the Study:

  • To investigate thermalization and quantum statistical properties in isolated spin chains.
  • To compare integrable and generic nonintegrable spin-chain models.
  • To analyze the role of observables and finite-size scaling in thermalization.

Main Methods:

  • Study of several observables in isolated spin-chain systems.
  • Analysis of both integrable and generic nonintegrable models.
  • Application of finite-size scaling analysis.
  • Examination of diagonal and off-diagonal matrix elements.

Main Results:

  • Nonintegrable models' diagonal matrix elements align with the eigenstate thermalization hypothesis.
  • Integrable systems show deviations from ETH, resembling noninteracting many-fermion models.
  • Finite-size scaling indicates a crossover scale related to scattering length.
  • Low-frequency off-diagonal elements in generic systems follow ETH-analogous behavior.

Conclusions:

  • Integrable spin chains exhibit distinct thermalization properties compared to nonintegrable ones.
  • The scattering length plays a key role in the crossover between thermalization regimes.
  • Deviations in integrable systems highlight the limitations of ETH in certain quantum many-body scenarios.