Adiabatic approximation in the second quantized formulation
arXiv:0710.5341 · doi:10.1103/PhysRevD.77.045006
Abstract
Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders and a model related to the geometric phase which can be exactly diagonalized in the present sense.
16 pages
References in corpus (13)
- Inconsistency in the application of the adiabatic theorem
- Quantitative conditions do not guarantee the validity of the adiabatic approximation
- Sufficiency Criterion for the Validity of the Adiabatic Approximation
- Validity of Quantum Adiabatic Theorem
- A new perturbative approach to the adiabatic approximation
- Validity of adiabaticity in Cavity QED
- Second quantized formulation of geometric phases
- Geometric phases and hidden local gauge symmetry
- A note on the geometric phase in adiabatic approximation
- Perturbative Analysis of Possible Failures in the Traditional Adiabatic Conditions
- Topological properties of Berry's phase
- Geometric phases for mixed states and decoherence
- Geometric phases, gauge symmetries and ray representation
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- Matrix Operator Approach to the Quantum Evolution Operator and the Geometric Phase
- Geometric phase and chiral anomaly; their basic differences