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Related Concept Videos

Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
Diamagnetism01:26

Diamagnetism

Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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...
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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...

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Updated: Jun 16, 2026

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains
07:42

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Published on: July 20, 2022

Fermionic mean-field dynamics for spin systems beyond free fermions.

Rishab Dutta1, Marc Illa1, Niranjan Govind1,2

  • 1Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99354, USA.

The Journal of Chemical Physics
|June 15, 2026
PubMed
Summary
This summary is machine-generated.

We present fermionized time-dependent Hartree-Fock (fTDHF), a new quantum dynamics method for spin-1/2 systems. This efficient approach accurately simulates complex quantum behaviors on classical computers.

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Study of Protein Dynamics via Neutron Spin Echo Spectroscopy
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Study of Protein Dynamics via Neutron Spin Echo Spectroscopy

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Condensed matter theory

Background:

  • Simulating real-time quantum dynamics is computationally challenging.
  • Spin-1/2 systems exhibit complex behaviors due to interactions and correlations.
  • Existing methods struggle with long-range interactions and non-local operators.

Purpose of the Study:

  • Introduce a novel real-time quantum dynamics method, fermionized time-dependent Hartree-Fock (fTDHF).
  • Develop an efficient computational approach for spin-1/2 Hamiltonians.
  • Benchmark fTDHF against exact dynamics for various quantum phenomena.

Main Methods:

  • Map spin-1/2 Hamiltonians to fermions using the Jordan-Wigner transformation.
  • Employ fTDHF, a method handling non-local string operators via transition matrix elements.
  • Implement fTDHF on classical computers with polynomial scaling in system size and linear scaling in time steps.

Main Results:

  • fTDHF is formally equivalent to exact dynamics for free fermions.
  • The method efficiently handles non-local string operators from long-range interactions.
  • fTDHF reproduces qualitative dynamics of adiabatic state preparation, many-body localization, and particle production in benchmark models.

Conclusions:

  • fTDHF offers an efficient and scalable method for simulating quantum dynamics of spin-1/2 systems.
  • The mean-field nature of fTDHF provides a simple physical picture of complex quantum phenomena.
  • fTDHF demonstrates accuracy comparable to exact methods for diverse physical scenarios.