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Commutability between the semiclassical and adiabatic limits.

Biao Wu1, Jie Liu

  • 1Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China.

Physical Review Letters
|February 21, 2006
PubMed
Summary
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The commutability of adiabatic and semiclassical limits in many-boson systems changes with interaction strength. Strong interactions lead to incommutability, impacting theories like Gross-Pitaevskii equations.

Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Many-body systems

Background:

  • The adiabatic and semiclassical limits are crucial for understanding quantum systems.
  • Interacting many-boson systems exhibit complex behaviors influenced by mean-field interactions.
  • Bose-Einstein condensates are often described by nonlinear mean-field theories like Gross-Pitaevskii equations.

Purpose of the Study:

  • To investigate the relationship between the adiabatic and semiclassical limits in a many-boson system.
  • To determine how mean-field interaction strength affects the commutability of these limits.
  • To explore the implications of this commutability change on theoretical models.

Main Methods:

  • Utilized a second-quantized two-mode model for a many-boson interacting system.

Related Experiment Videos

  • Analyzed the system's behavior under varying strengths of mean-field interaction.
  • Examined the topological structure of energy bands to understand the transition.

    • Main Results:

    • The adiabatic and semiclassical limits are commutable for small mean-field interactions.
    • A critical interaction strength was identified where these limits become incommutable.
    • This change in commutability correlates with a topological alteration in energy band structures.

    Conclusions:

    • The commutability of adiabatic and semiclassical limits is sensitive to interaction strength.
    • Topological changes in energy bands signify a fundamental shift in system behavior.
    • Nonlinear mean-field theories may not be universally valid, particularly in the adiabatic limit for strongly interacting systems.