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Atomic Nuclei: Nuclear Relaxation Processes

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...

Ferromagnetism

Ferromagnetism

Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic dipoles are rigidly aligned in the same direction within a domain by quantum mechanical coupling among the atoms. This coupling is so strong that even thermal agitation at room temperature cannot break it. The result is that each domain has a net dipole moment. However, some materials have weaker coupling, and are ferromagnetic at lower...

Atomic Nuclei: Nuclear Spin State Overview

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 Spin State Population Distribution

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.

Paramagnetism

Paramagnetism

Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...

Diamagnetism

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.

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Related Experiment Video

Updated: May 18, 2026

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe₁₊_YTe Using a Spin-polarized Scanning Tunneling Microscope

Published on: March 24, 2019

Quantum annealing with antiferromagnetic fluctuations.

Yuya Seki¹, Hidetoshi Nishimori

¹Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

Introducing antiferromagnetic quantum fluctuations to quantum annealing improves efficiency for the p-spin model. This method avoids problematic first-order transitions, enabling faster ground state discovery.

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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

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Area of Science:

Quantum physics
Computational complexity
Condensed matter theory

Background:

Quantum annealing is a metaheuristic optimization algorithm.
The transverse-field quantum annealing struggles with first-order phase transitions in the p-spin model.
Efficiently finding ground states of complex models is a significant challenge.

Purpose of the Study:

To investigate the impact of antiferromagnetic quantum fluctuations on quantum annealing for the p-spin model.
To identify quantum paths that avoid first-order transitions.
To assess the potential for efficient computation of ground states.

Main Methods:

Introducing antiferromagnetic quantum fluctuations alongside the transverse-field term in quantum annealing.
Analytical and numerical studies of the p-spin model's phase diagram.
Utilizing the static approximation.
Investigating the energy gap between ground and excited states.

Main Results:

A quantum path avoiding first-order transitions was identified for intermediate p values.
Numerical evidence suggests polynomial time complexity at a second-order transition point.
Antiferromagnetic fluctuations enable efficient ground state finding, unlike transverse-field only methods.

Conclusions:

Antiferromagnetic quantum fluctuations enhance quantum annealing for the p-spin model.
This approach offers an efficient method for solving problems with intermediate p values.
The findings suggest quantum annealing can overcome limitations posed by first-order transitions.