A note on the geometric phase in adiabatic approximation
arXiv:quant-ph/0406163 · doi:10.1016/j.physleta.2005.03.043
Abstract
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough.
11 pages, no figure, modified and Journal-ref added
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Cited by in corpus (10)
- Quantitative conditions do not guarantee the validity of the adiabatic approximation
- Sufficiency Criterion for the Validity of the Adiabatic Approximation
- A new perturbative approach to the adiabatic approximation
- Validity of the Adiabatic Approximation
- Geometric phase for SU(N) through fiber bundles and unitary integration
- Engineering adiabaticity at an avoided crossing with optimal control
- Adiabatic approximation in the second quantized formulation
- On spin evolution in a time-dependent magnetic field: post-adiabatic corrections and geometric phases
- General conditions for a quantum adiabatic evolution
- Two geometric phases can dramatically differ from each other even if their evolution paths are sufficiently close in a pointwise manner