Some new forms of the adiabatic theorem: finite temperature and energy gap regularization

In the talk I consider some new questions related to the adiabatic theorem. First, we extend the notion of quantum adiabaticity to closed quantum systems initially prepared at finite temperature. In this case adiabaticity implies that the (mixed) state of the system stays close to a so-called quasi-Gibbs state, which is diagonal in the basis of instantaneous eigenstates of the Hamiltonian. Second, we discuss the dependence of the efficiency of the adiabatic approximation on the structure of the Hamiltonian. In this context I consider theorems showing that the efficiency of the adiabatic approximation is more influenced by eigenvectors change rate than by size of energy gap.