A Solved Model to Show Insufficiency of Quantitative Adiabatic Condition

The adiabatic theorem is a useful tool in processing quantum systems slowly evolving, but its practical application depends on the quantitative condition expressed by Hamiltonian's eigenvalues and eigenstates, which is usually taken as a sufficient condition. Recently, the sufficiency of the condition was questioned, and several counterexamples have been reported. Here we present a new solved model to show the insufficiency of the traditional quantitative adiabatic condition.