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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.1K
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...
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

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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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Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

1.2K
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,...
1.2K
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

2.5K
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...
2.5K
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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1.2K
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.
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1.2K
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

1.5K
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.
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Unveiling Operator Growth Using Spin Correlation Functions.

Matteo Carrega1, Joonho Kim2, Dario Rosa3,4

  • 1NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy.

Entropy (Basel, Switzerland)
|June 2, 2021
PubMed
Summary
This summary is machine-generated.

We studied non-equilibrium dynamics in quantum systems using a Sachdev-Ye-Kitaev (SYK) model quench. Our findings show spin-spin correlation functions can reveal quantum chaos by distinguishing operator growth from hopping dynamics.

Keywords:
operator growthquantum chaosquantum quenchscrambling

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Area of Science:

  • Quantum Physics
  • Many-Body Systems
  • Condensed Matter Theory

Background:

  • Strongly correlated Hamiltonians with all-to-all interactions exhibit complex non-equilibrium dynamics.
  • Understanding quantum chaos is crucial for characterizing many-body quantum systems.

Purpose of the Study:

  • To investigate non-equilibrium dynamics after a quantum quench in a Sachdev-Ye-Kitaev (SYK)-based model.
  • To determine if spin-spin correlation functions can distinguish between operator growth and operator hopping dynamics.

Main Methods:

  • Utilized a Sachdev-Ye-Kitaev (SYK)-based quench protocol.
  • Analyzed the time evolution of spin-spin correlation functions.
  • Investigated the sensitivity of correlation functions to operator k-locality.

Main Results:

  • Time evolution of spin-spin correlation functions is sensitive to operator k-locality.
  • Successfully distinguished operator growth dynamics from operator hopping.
  • Operator growth dynamics identified as a hallmark of quantum chaos.

Conclusions:

  • Spin-spin correlation function decay can serve as a tool to probe quantum chaos.
  • This method offers a promising avenue for studying the emergence of chaotic behavior in quench setups.
  • The findings are accessible in state-of-the-art experimental quench setups.