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Related Concept Videos

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...
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: 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...
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,...
Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of motion,...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

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Related Experiment Video

Updated: May 11, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Universal spatial correlations in random spinor fields.

Juan Diego Urbina1, Michael Wimmer, Dominik Bauernfeind

  • 1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 18, 2013
PubMed
Summary
This summary is machine-generated.

We discovered universal spatial fluctuations in systems with complex spin dynamics. These findings, derived from numerical calculations, offer insights into electron gas behavior and spin-orbit interactions.

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Last Updated: May 11, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Area of Science:

  • Condensed matter physics
  • Quantum mechanics

Background:

  • Systems with nontrivial spin dynamics exhibit complex behaviors.
  • Understanding spatial fluctuations is crucial for characterizing these systems.

Purpose of the Study:

  • To identify universal spatial fluctuations in systems with nontrivial spin dynamics.
  • To investigate correlations in electron gases with spin-orbit interaction.

Main Methods:

  • Exact numerical diagonalization was employed.
  • Calculated correlations between spinor amplitudes, spin polarizations, and spin currents.
  • Analyzed bulk and boundary properties of a confined 2D electron gas.

Main Results:

  • Identified universal spatial fluctuations.
  • Numerical results showed excellent agreement with system-independent spatial correlations.
  • Established a link between universal predictions and response functions.

Conclusions:

  • The study confirms the universality of spatial fluctuations in the studied systems.
  • Results provide a physical interpretation within linear response theory.
  • Findings are relevant for understanding electron gas behavior with spin-orbit interaction.