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Related Concept Videos

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

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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.
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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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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.
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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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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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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Solitons in Bose-Einstein Condensates with Helicoidal Spin-Orbit Coupling.

Yaroslav V Kartashov1,2,3, Vladimir V Konotop4

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Stable, freely moving solitons exist in Bose-Einstein condensates with spin-orbit coupling, even with varying parameters. These solitons exhibit elastic interactions, with Zeeman splitting causing inelastic collisions.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Nonlinear dynamics

Background:

  • Bose-Einstein condensates (BECs) are quantum states of matter.
  • Spin-orbit (SO) coupling influences BEC properties.
  • Solitons are stable, localized wave packets.

Purpose of the Study:

  • Investigate the existence and stability of freely moving solitons.
  • Analyze soliton behavior in spatially inhomogeneous BECs with helicoidal SO coupling.
  • Examine the impact of Zeeman splitting on soliton dynamics.

Main Methods:

  • Theoretical analysis using coupled Gross-Pitaevskii equations.
  • Study of solitons in a rotating frame to simplify SO coupling.
  • Exact solutions derived for soliton families.

Main Results:

  • Stable propagating solitons found in inhomogeneous BECs with helicoidal SO coupling.
  • In the absence of Zeeman splitting, solitons exhibit integrable system properties and elastic interactions.
  • Zeeman splitting leads to two families of moving solitons with inelastic collisions.

Conclusions:

  • Freely moving, stable solitons can exist in complex BEC systems.
  • SO coupling and Zeeman splitting significantly alter soliton dynamics.
  • The system offers a platform for studying nonlinear phenomena in quantum systems.