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Sufficiency criterion for the validity of the adiabatic approximation
1Department of Physics, National University of Singapore, 10 Kent Ridge Crescent, Singapore. phytdm@nus.edu.sg
Physical Review Letters
|May 16, 2007
Summary
The standard quantitative condition for adiabatic approximation is sufficient for some quantum systems but not all. A general criterion, including additional conditions, ensures adiabatic approximation validity for all quantum systems.
Area of Science:
- Quantum mechanics
- Theoretical physics
Background:
- The adiabatic approximation is crucial in quantum mechanics.
- A widely used quantitative condition for this approximation has recently shown limitations.
Purpose of the Study:
- To re-evaluate the sufficiency of the standard quantitative condition for the adiabatic approximation.
- To develop a more general and universally applicable criterion for adiabatic approximation validity.
Main Methods:
- Analysis of the quantitative condition for adiabatic approximation.
- Development of a generalized criterion incorporating additional conditions.
- Application of the criterion to various physical models.
Main Results:
- The standard quantitative condition is sufficient for a specific subset of quantum mechanical systems.
- For general quantum systems, the standard condition alone is insufficient.
- A refined criterion, combining the standard condition with additional requirements, proves sufficient for all N-dimensional quantum systems.
Conclusions:
- The generalized quantitative criterion provides a robust framework for assessing adiabatic approximation validity.
- This new criterion enhances the applicability and reliability of adiabatic approximations in diverse quantum systems.
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