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Related Concept Videos

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,...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
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...
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...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
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.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

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Nonequilibrium Kondo model: crossover from weak to strong coupling.

Mikhail Pletyukhov1, Herbert Schoeller

  • 1Institut für Theorie der Statistischen Physik, RWTH Aachen, 52056 Aachen, Germany. pletmikh@physik.rwth-aachen.de

Physical Review Letters
|September 26, 2012
PubMed
Summary

This study introduces a new real-time renormalization group method to analyze the nonequilibrium Kondo model. The findings reveal universal spin dynamics and conductance line shapes, agreeing with existing theories and experiments.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Spin Dynamics

Background:

  • The Kondo model describes magnetic impurities in metals, crucial for understanding electron correlations.
  • Nonequilibrium phenomena in quantum systems are vital for developing novel electronic devices.
  • Understanding spin relaxation and transport properties is key to quantum information technologies.

Purpose of the Study:

  • To develop and apply a novel real-time renormalization group (RTRG) method for analyzing the nonequilibrium Kondo model.
  • To investigate the energy-dependent spin relaxation rate and nonlinear conductance at finite voltage and temperature.
  • To derive universal line shapes for conductance and analyze transient spin dynamics.

Main Methods:

  • A new formulation of the real-time renormalization group (RTRG) method using the Laplace variable as a flow parameter.
  • Evaluation of energy-dependent spin relaxation rate and nonlinear conductance.
  • Derivation of approximate universal line shapes for conductance across the weak-to-strong coupling crossover.

Main Results:

  • The derived nonlinear conductance line shapes show excellent agreement with exact equilibrium methods, Fermi-liquid theory, weak-coupling expansions, and recent experimental results.
  • Transient spin dynamics exhibit a universal exponential decay in the long-time limit, with a truncation-dependent pre-exponential power law.
  • For multichannel Kondo models, a pure power-law decay, characteristic of non-Fermi-liquid behavior, is predicted.

Conclusions:

  • The developed RTRG method provides a powerful tool for studying nonequilibrium quantum phenomena.
  • The study establishes universal features in spin relaxation and conductance for the Kondo model.
  • Predictions for multichannel models suggest potential for observing non-Fermi-liquid behavior in future experiments.