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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

2.5K
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.
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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

1.3K
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.
1.3K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

2.1K
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...
2.1K
Atomic Nuclei: Nuclear Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

3.5K
All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
3.5K
Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

1.3K
The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
1.3K
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

1.1K
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
1.1K

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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

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Generalized Mean Fields for Trapped Atomic Bose-Einstein Condensates.

N P Proukakis1, K Burnett1

  • 1Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.

Journal of Research of the National Institute of Standards and Technology
|January 1, 1996
PubMed
Summary
This summary is machine-generated.

We present new equations for partially condensed atoms, enabling the study of order parameters and mean fields in trapped, cooled atomic samples. This formalism handles the evolution of mean fields using two-loop kinetics.

Keywords:
Hartree-Fock-Bogoliubov approximationevaporative coolingkinetics of Bose-Einstein condensationmean-field theorynonlinear Schrödinger equation

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Area of Science:

  • Atomic physics
  • Quantum mechanics
  • Statistical mechanics

Background:

  • Partially condensed atomic samples present complex behaviors.
  • Understanding order parameters and mean fields is crucial.

Purpose of the Study:

  • To describe generalized time-dependent mean-field equations for partially condensed atomic samples.
  • To provide a method for investigating order parameters and mean fields.
  • To develop a closed system of self-consistent equations.

Main Methods:

  • Derivation of generalized time-dependent mean-field equations.
  • Utilizing an equation of motion method.
  • Constructing a formalism for two-loop kinetics.

Main Results:

  • A closed system of self-consistent equations for order parameters.
  • The derived equations reduce to existing treatments in various limits.
  • A formalism to handle mean field evolution due to two-loop kinetics.

Conclusions:

  • The generalized equations offer a comprehensive approach to studying partially condensed atomic systems.
  • The formalism accommodates complex kinetic evolutions.
  • This work unifies and extends existing theoretical frameworks.