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From the cover: temperature, ordering, and equilibrium with time-dependent confining forces.

J P Schiffer1, M Drewsen, J S Hangst

  • 1Argonne National Laboratory, Argonne, IL 60439, USA.

Proceedings of the National Academy of Sciences of the United States of America
|September 20, 2000
PubMed
Summary

Temperature and equilibrium are ill-defined for systems with time-varying forces. Simulations show equilibrium is reached when considering only secular motion, with coupling increasing quadratically with temperature.

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Area of Science:

  • Atomic Physics
  • Quantum Mechanics
  • Thermodynamics

Background:

  • Temperature and equilibrium concepts are challenging in systems with time-varying external forces.
  • Radio frequency ion traps with laser-cooled ions provide a model system for studying these phenomena.
  • Ions in such traps can exhibit sub-mK temperatures while possessing kinetic energies orders of magnitude higher due to coherent motion.

Purpose of the Study:

  • To investigate the definitions of temperature and equilibrium in driven systems.
  • To understand the conditions under which equilibrium is achieved in a radio frequency ion trap.
  • To quantify the coupling between driven and random ion motion.

Main Methods:

  • Simulations of 1,000 ions in a radio frequency ion trap.

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  • Analysis of kinetic energies and displacements.
  • Focus on secular motion (aperiodic displacements) and driven motion (periodic confinement).

    • Main Results:

    • Equilibrium between degrees of freedom is achieved when only secular motion is considered.
    • The coupling between periodic driven motion and nonperiodic random motion is minimal at low temperatures.
    • This coupling increases quadratically with temperature.

    Conclusions:

    • Standard definitions of temperature and equilibrium require careful consideration in driven systems.
    • Secular motion plays a crucial role in achieving apparent equilibrium.
    • The temperature dependence of coupling is a key characteristic of these systems.