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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...
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: 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...
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: 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.
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Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...

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Related Experiment Video

Updated: May 9, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Transitionless quantum driving for spin systems.

Kazutaka Takahashi1

  • 1Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 16, 2013
PubMed
Summary
This summary is machine-generated.

We introduce transitionless quantum driving for spin systems, constructing Hamiltonians to preserve adiabatic states. This method addresses challenges in quantum phase transitions for many-body systems.

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Last Updated: May 9, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Published on: March 30, 2017

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

  • Quantum mechanics
  • Spin systems
  • Quantum driving

Background:

  • Time-dependent quantum systems require precise control.
  • Adiabatic states are crucial for maintaining system integrity.
  • Spin systems are fundamental in quantum information and condensed matter physics.

Purpose of the Study:

  • To apply transitionless quantum driving to spin systems.
  • To construct driving Hamiltonians that preserve adiabatic states.
  • To explore applications in quantum phase transitions.

Main Methods:

  • Developing a driving Hamiltonian for a given system Hamiltonian.
  • Ensuring adiabatic states of the original system follow the Schrödinger equation.
  • Explicitly constructing driving Hamiltonians for the XY spin chain and Lipkin-Meshkov-Glick model.

Main Results:

  • Successfully constructed driving Hamiltonians for specific spin systems.
  • Identified conditions for time-independent and equivalent driving Hamiltonians.
  • Proposed a method to circumvent issues at quantum phase transition points.

Conclusions:

  • Transitionless quantum driving is a viable method for controlling spin systems.
  • The approach offers a way to navigate quantum phase transitions.
  • Further research can explore time-independent and equivalent driving Hamiltonians.