A quantum KAM-like theorem II: fundamentals of localisation in quantum theory for resonance states

The quantum KAM-like theorem is extended to resonance states. The formulation uses dilation analysis and existence condition of a unique transformation between eigenstates of integrable and non-integrable Hamiltonians. This condition determines the ability to assign local quantum numbers to eigenstates of non-integrable Hamiltonians and explains localisation phenomena. (author)