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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Range00:59

Range

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The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
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Spin–Spin Coupling Constant: Overview01:08

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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.
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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NMR Spectroscopy: Spin–Spin Coupling01:08

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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...
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Spin–Spin Coupling: One-Bond Coupling01:17

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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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Study of Protein Dynamics via Neutron Spin Echo Spectroscopy
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Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains.

Fangli Liu1, Rex Lundgren1, Paraj Titum1,2

  • 1Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters
|May 4, 2019
PubMed
Summary
This summary is machine-generated.

Long-range interactions in the Ising model create bound quasiparticles, similar to mesons. Their masses can be measured via order parameter dynamics after a quench, impacting thermalization.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • The transverse-field Ising model is a fundamental model in condensed matter physics.
  • Understanding quasiparticle excitations and dynamics is crucial for characterizing quantum systems.
  • The effects of long-range interactions on quantum models are not fully understood.

Purpose of the Study:

  • To investigate quasiparticle excitation and quench dynamics in a 1D transverse-field Ising model with power-law interactions.
  • To explore the consequences of long-range interactions on confinement and bound states.
  • To identify experimental signatures and measurement techniques for these phenomena.

Main Methods:

  • Analytical study of the one-dimensional transverse-field Ising model with power-law interactions (1/r^{α}).
  • Analysis of quasiparticle excitation and quench dynamics.
  • Development of a two-kink model to explain confinement and predict quasiparticle masses.
  • Investigation of order parameter dynamics and Fourier spectra.

Main Results:

  • Long-range interactions induce a confining potential, binding domain walls into quasiparticles analogous to mesons.
  • These quasiparticles exhibit distinct signatures in order parameter dynamics after a global quench.
  • The Fourier spectrum of order parameters serves as a direct probe for quasiparticle masses.
  • A two-kink model accurately predicts the masses of these bound quasiparticles.
  • Quasiparticle states can cause slow thermalization of observables for specific initial states.

Conclusions:

  • Long-range interactions fundamentally alter the behavior of the Ising model, leading to emergent bound states.
  • The identified quasiparticles and their mass-measurement techniques are experimentally relevant for trapped-ion systems.
  • This work provides a theoretical framework for understanding confinement and its impact on thermalization in quantum systems.