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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.
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Phase Transitions: Vaporization and Condensation02:39

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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase...
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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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Related Experiment Video

Updated: May 1, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

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Thermalization of field driven quantum systems.

H Fotso1, K Mikelsons1, J K Freericks1

  • 1Department of Physics, Georgetown University, 37th and O Sts. NW, Washington, DC 20057 USA.

Scientific Reports
|April 17, 2014
PubMed
Summary
This summary is machine-generated.

Quantum systems exhibit five distinct behaviors when driven by a DC electric field, revealing richer dynamics than previously understood. Integrability in the absence of a field does not dictate thermalization outcomes.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Quantum systems typically do not thermalize due to unitary evolution.
  • The eigenstate thermalization hypothesis explains thermalization by assuming observables are constant within energy windows.
  • Integrable systems violate this hypothesis due to numerous conserved quantities.

Purpose of the Study:

  • To investigate the thermalization behavior of quantum systems subjected to a DC electric field.
  • To identify and categorize the generic dynamic behaviors under such driving.
  • To compare these behaviors in the Hubbard and Falicov-Kimball models.

Main Methods:

  • Theoretical analysis of quantum systems driven by a DC electric field.
  • Examination of the Hubbard and Falicov-Kimball models.
  • Classification of observed dynamic behaviors into five generic scenarios.

Main Results:

  • Five generic behaviors were identified: monotonic/oscillatory approach to infinite temperature, monotonic/oscillatory approach to a nonthermal steady state, and evolution to an oscillatory state.
  • Both the Hubbard and Falicov-Kimball models exhibited the first four scenarios.
  • Only the Hubbard model displayed the fifth oscillatory state behavior.
  • Integrability in the absence of a field was found to be irrelevant to these outcomes.

Conclusions:

  • DC electric field driving induces significantly richer thermalization dynamics in quantum systems than previously observed.
  • The presence or absence of integrability in the static system does not determine the observed dynamic behaviors under a DC field.
  • These findings challenge existing paradigms and offer new insights into quantum thermalization.