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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

1.1K
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.
1.1K
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

712
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.
712
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.1K
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...
1.1K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.0K
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...
1.0K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

1.1K
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...
1.1K
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

1.6K
The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
1.6K

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Updated: Sep 6, 2025

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
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In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

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Absence of Superdiffusion in Certain Random Spin Models.

Pieter W Claeys1, Austen Lamacraft1, Jonah Herzog-Arbeitman1

  • 1TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.

Physical Review Letters
|July 1, 2022
PubMed
Summary
This summary is machine-generated.

Spin transport in fluctuating Heisenberg chains exhibits normal diffusion at long times, with an increased diffusion constant. This study analyzes spin dynamics in a disordered spin-1/2 chain, moving beyond integrable models.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Spin Systems
  • Statistical Mechanics

Background:

  • Spin dynamics in spin-1/2 Heisenberg chains are typically superdiffusive.
  • Integrable models and SU(2) symmetry are key in theoretical approaches.
  • Breaking integrability necessitates new analytical methods.

Purpose of the Study:

  • Investigate spin transport in a spin-1/2 Heisenberg chain with fluctuating exchange couplings.
  • Analyze the impact of spatial and temporal noise on spin dynamics.
  • Extend theoretical understanding beyond integrable systems.

Main Methods:

  • Perturbation theory expansion in the mean coupling J for strong noise and infinite temperature.
  • Analysis of operator dynamics in the strong noise limit.
  • Comparison with matrix product operator simulations for finite-time dynamics.

Main Results:

  • Regular diffusion is observed at long times despite broken integrability.
  • The diffusion constant is enhanced compared to non-disordered systems.
  • Finite-time spin dynamics are characterized and validated against simulations.

Conclusions:

  • Fluctuating exchange couplings lead to diffusive spin transport, contrasting with superdiffusion in integrable chains.
  • Perturbation theory provides a viable framework for analyzing disordered spin systems.
  • The model offers insights into non-integrable quantum spin dynamics.