Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-06-10
Phys.Rev. A55 (1997) 1653-1664
Physics
High Energy Physics
High Energy Physics - Theory
uuencoded LaTeX file, 19 pages
Scientific paper
10.1103/PhysRevA.55.1653
A precise definition of an adiabaticity parameter $\nu$ of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator $U(\tau)=\sum_\ell U^{(\ell)}(\tau)$ with $U^{(\ell)}(\tau)$ being at least of the order $\nu^\ell$. In particular $U^{(0)}(\tau)$ corresponds to the adiabatic approximation and yields Berry's adiabatic phase. It is shown that this series expansion has nothing to do with the $1/\tau$-expansion of $U(\tau)$. It is also shown that the non-adiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. Some related issues concerning the geometric phase are also discussed.
No associations
LandOfFree
The Quantum Adiabatic Approximation and the Geometric Phase does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Quantum Adiabatic Approximation and the Geometric Phase, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Quantum Adiabatic Approximation and the Geometric Phase will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-100956