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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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

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

NMR Spectroscopy: Spin–Spin Coupling

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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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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Genuine quantum scars in many-body spin systems.

Andrea Pizzi1,2, Long-Hei Kwan3, Bertrand Evrard4

  • 1Cavendish Laboratory, University of Cambridge, Cambridge, UK. ap2076@cam.ac.uk.

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|July 21, 2025
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Summary
This summary is machine-generated.

Quantum mechanics introduces "scarring" in many-body systems, preserving memory of initial states. This phenomenon weakly breaks ergodicity, revealing underlying structure despite chaotic behavior in quantum simulations.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Classical chaos leads to rapid thermalization and loss of initial state information in many-body systems.
  • The Eigenstate Thermalization Hypothesis (ETH) posits that quantum eigenstates in thermalizing systems are locally thermal and feature extensive entanglement.

Purpose of the Study:

  • To investigate how quantum mechanics influences chaos and thermalization in many-body systems.
  • To identify and characterize quantum phenomena that preserve information about the system's past, challenging complete thermalization.

Main Methods:

  • Analysis of quantum eigenstates in many-body systems, focusing on their distribution and entanglement properties.
  • Identification of 'scarred' eigenstates with enhanced weight along classical unstable periodic orbits.
  • Examination of a diverse range of spin models, including prominent condensed matter systems.

Main Results:

  • Quantum eigenstates, despite being thermal and entangled, exhibit 'quantum scarring'.
  • Exponentially many eigenstates are scarred, meaning they retain significant weight along classical periodic orbits.
  • This scarring allows systems to retain memory of their initial conditions, weakly breaking ergodicity even in fully thermal states.

Conclusions:

  • Quantum scarring is a ubiquitous phenomenon in many-body quantum systems, demonstrating structure amidst chaos.
  • This finding challenges the complete loss of information predicted by classical chaos and ETH in certain quantum regimes.
  • The results have implications for understanding information dynamics and designing experiments in quantum simulators.