Slow dynamics for self-adjoint semigroups and unitary evolution groups

Abstract

It is shown that the time-average quantum return probability of (Baire) generic states of systems with purely α-Hausdorff continuous spectrum has an oscillating behaviour between a (maximum) fast power-law decay and a (minimum) slow power-law decay. As an application, a new result on the quantum dynamics of Schrödinger operators with limit-periodic potentials is presented.