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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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

Atomic Nuclei: Nuclear Relaxation Processes

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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.
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Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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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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Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

1.5K
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...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

1.3K
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.
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Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
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Related Experiment Video

Updated: Nov 12, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Quantum chaos, equilibration, and control in extremely short spin chains.

Nicolás Mirkin1, Diego Wisniacki1

  • 1Departamento de Física J. J. Giambiagi and IFIBA, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina.

Physical Review. E
|March 19, 2021
PubMed
Summary

Even small quantum systems can exhibit chaos. Researchers monitored a single spin

Area of Science:

  • Quantum physics
  • Statistical mechanics

Background:

  • Open quantum systems are typically modeled as large many-body systems.
  • The complexity required for internal equilibration in isolated many-body quantum systems remains an open question.

Purpose of the Study:

  • To investigate the conditions for internal equilibration in isolated many-body quantum systems.
  • To sense chaotic behavior in generic spin chains using purity degradation of a single spin.

Main Methods:

  • Monitoring purity degradation of a single spin.
  • Analyzing spin chains of varying lengths, including very short chains of three spins.

Main Results:

  • Chaotic behavior in generic spin chains can be detected by monitoring a single coupled spin's purity.

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Last Updated: Nov 12, 2025

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  • The integrable to chaos transition was reproduced in extremely short spin chains (three spins).
  • Quantum chaos influences the degree of control in quantum control experiments, even in small systems.

    • Conclusions:

    • Internal equilibration and chaos can emerge in surprisingly small many-body quantum systems.
    • Purity degradation is a sensitive probe for quantum chaos.
    • Understanding quantum chaos is crucial for advancing quantum control.