Sufficient conditions for quantum adiabatic approximation

摘要

Roughly speaking quantum adiabatic approximation states that in some cases the system state will be approximately a corresponding instantaneous eigenstate if at the initial time the system is in an eigenstate of the initial hamiltonian. We divide quantum adiabatic approximation into two kinds, one does not concern the phase change of the system state while the other does, and discuss sufficient conditions respectively. Additionally we give a proof of quantum adiabatic theorem.