ﻻ يوجد ملخص باللغة العربية
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix valued quantum Hamiltonians. The results are illustrated by several physical relevant examples.
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to
We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the standard criterion for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue tha
We study the gauge invariance of laser-matter interaction. The velocity gauge where the vector potential is expanded to the $n$-th order with respect to the spatial coordinate, and the length gauge where the electric and magnetic fields are expanded
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
We restate the adiabatic elimination approximation as the first term in a singular perturbation expansion. We use the invariant manifold formalism for singular perturbations in dynamical systems to identify systematic improvements on adiabatic elimin