Quantum adiabatic theorem with energy gap regularization

The talk deals with the adiabatic approximation of quantum dynamics. It is usually believed that one of the principal factors determining its stability is the structure of the spectrum. As the adiabatic theorem states in its usual formulation, deviations from the adiabatic evolution can be estimated from above by the ratio of Hamiltonian change rate to the energy gap size in the spectrum. The talk is devoted to discussing this dependence and, in particular, to theorems showing that the efficiency of the adiabatic approximation is more influenced by the eigenvectors change rate than by the size of energy gap.