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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...
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,...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

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:
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.
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

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Related Experiment Video

Updated: Jun 14, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

Transitions in eigenvalue and wavefunction structure in (1+2) -body random matrix ensembles with spin.

Manan Vyas1, V K B Kota, N D Chavda

  • 1Physical Research Laboratory, Ahmedabad 380 009, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Finite interacting Fermi systems exhibit a transition from Poisson to GOE as interaction strength increases. This study models these systems using random matrix theory, revealing a duality region corresponding to thermalization.

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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

Related Experiment Videos

Last Updated: Jun 14, 2026

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

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

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Nuclear physics

Background:

  • Finite interacting Fermi systems are fundamental in understanding complex quantum phenomena.
  • Mean-field and two-body interactions significantly influence system dynamics and spectral properties.
  • Random matrix theory provides a powerful framework for modeling chaotic quantum systems.

Purpose of the Study:

  • To model finite interacting Fermi systems using the embedded Gaussian orthogonal ensemble with spin (EGOE(1+2)-s).
  • To investigate the transitions in spectral fluctuations and strength functions with increasing interaction strength (lambda).
  • To identify and characterize a duality region and its connection to thermalization.

Main Methods:

  • Utilized numerical calculations based on the EGOE(1+2)-s random matrix model.
  • Analyzed level fluctuations for Poisson to GOE transitions.
  • Examined strength functions for Breit-Wigner to Gaussian transitions.
  • Derived a propagator for spectral variances to describe spin dependence of transition points.
  • Compared single-particle, information, and thermodynamic entropy to identify thermalization.

Main Results:

  • Demonstrated a generic transition from Poisson to GOE in level fluctuations as lambda increases.
  • Observed a Breit-Wigner to Gaussian transition in strength functions with increasing lambda.
  • Identified a duality region where information entropy is consistent across different bases.
  • Established that this duality region corresponds to thermalization, evidenced by entropy comparisons.

Conclusions:

  • The EGOE(1+2)-s model effectively captures the transition to chaos in finite Fermi systems.
  • The interaction strength (lambda) governs the transition from regular to chaotic behavior.
  • The identified duality region serves as a signature of thermalization in these quantum systems.