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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

1.4K
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.
1.4K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

1.3K
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...
1.3K
Phase Transitions02:31

Phase Transitions

20.9K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
20.9K
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...
1.1K
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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

Atomic Nuclei: Nuclear Relaxation Processes

774
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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Related Experiment Video

Updated: Oct 17, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Dynamical quantum phase transitions in the spin-boson model.

David Dolgitzer, Debing Zeng, Yusui Chen

    Optics Express
    |October 7, 2021
    PubMed
    Summary

    Dynamical quantum phase transitions in a two-qubit system were studied. The rate function

    Area of Science:

    • Quantum Physics
    • Open Quantum Systems
    • Quantum Phase Transitions

    Background:

    • Dynamical quantum phase transitions (DQPTs) are crucial for understanding non-equilibrium quantum systems.
    • Open quantum systems exhibit complex dynamics influenced by their environment.

    Purpose of the Study:

    • To investigate DQPTs in a 2-qubit system coupled to a transverse field and a bosonic environment.
    • To analyze the influence of environmental memory and coupling strength on DQPT dynamics.

    Main Methods:

    • Stochastic Schrödinger equation approach for numerical simulation.
    • Analysis of the Loschmidt echo rate function dynamics.

    Main Results:

    • Nonanalyticity in the rate function of the Loschmidt echo observed during sudden quenches of the transverse field.

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  • Environmental memory time and system-field coupling strength jointly affect the rate function dynamics.

    • Conclusions:

    • The study reveals key factors influencing DQPTs in a 2-qubit open system.
    • A semi-classical explanation connects many-body DQPTs with non-Markovian open quantum system dynamics.