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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

34.7K
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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Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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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...
912
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.0K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.0K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

938
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...
938
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

1.0K
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...
1.0K
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

1.4K
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...
1.4K

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Updated: Jun 27, 2025

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots
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Controllable quantum scars induced by spin-orbit couplings in quantum dots.

Lin Zhang1, Yutao Hu1, Zhao Yao1

  • 1School of Physics, Central South University, Changsha, 410083, China.

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|April 29, 2024
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Summary
This summary is machine-generated.

Spin-orbit couplings (SOCs) in quantum dots create quantum scar states. These scars, bridging classical and quantum mechanics, are controllable and robust, offering insights into relativistic effects.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Relativistic quantum mechanics

Background:

  • Spin-orbit couplings (SOCs) arise from relativistic corrections and introduce nonlinearity, driving chaotic dynamics in classical systems.
  • Quantum dots confined by parabolic potentials are model systems for studying quantum phenomena.

Purpose of the Study:

  • To investigate the emergence and properties of quantum scar states in a nanoscale quantum dot with SOCs.
  • To explore the relationship between classical chaos, relativistic effects, and quantum scar formation.
  • To determine the controllability and robustness of these quantum scars.

Main Methods:

  • Theoretical analysis of a quantum dot model with Rashba and Dresselhaus SOCs.
  • Examination of system eigenstates and electron density distributions.
  • Analysis of classical Hamilton's equations in the presence of SOCs.

Main Results:

  • Quantum scar states emerge quasi-periodically in eigenstates when confinement energies are nearly commensurable.
  • These scars exhibit both quantum interference and classical trajectory features.
  • Identical Rashba and Dresselhaus SOC strengths eliminate chaos and quantum scars by linearizing classical equations.
  • Quantum scars demonstrate robustness against small parameter perturbations.

Conclusions:

  • Quantum scars induced by SOCs serve as a bridge between classical and quantum behaviors.
  • The presence and disappearance of quantum scars are directly linked to the system's chaotic dynamics.
  • Quantum scars, particularly those induced by Rashba SOC, are controllable and detectable via external gating.