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Adiabatic condition for nonlinear systems.

Han Pu1, Peter Maenner, Weiping Zhang

  • 1Department of Physics and Astronomy, and Rice Quantum Institute, Rice University, Houston, Texas 77251-1892, USA.

Physical Review Letters
|March 16, 2007
PubMed
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The adiabatic approximation, crucial in quantum mechanics, needs a new derivation method for nonlinear systems. This study introduces a linearization technique to establish an analytic adiabatic condition for these complex scenarios.

Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Nonlinear dynamics

Background:

  • The adiabatic approximation is fundamental in quantum mechanics for linear systems.
  • Derivation relies on instantaneous eigenvalues and eigenstates, a method unsuitable for nonlinear systems.

Purpose of the Study:

  • To develop a method for deriving the adiabatic condition in nonlinear systems.
  • To establish an analytic adiabatic condition for nonlinear mean-field models.

Main Methods:

  • Linearization procedure applied to nonlinear systems.
  • Analysis of photoassociation of atoms into diatomic molecules as a model system.

Main Results:

  • Demonstrated a breakdown of standard methods in nonlinear systems.

Related Experiment Videos

  • Successfully derived an analytic adiabatic condition using linearization for the nonlinear model.

    • Conclusions:

    • Linearization is the correct approach for adiabatic conditions in nonlinear mean-field systems.
    • The derived analytic condition is applicable to models like atom photoassociation.