J.E. Avron and A. Elgart
The Adiabatic Theorem of Quantum Mechanics
(30K, LATeX 2e)
ABSTRACT. We prove the adiabatic theorem for quantum evolution without the traditional
gap condition. We show that the theorem holds essentially in all cases
where it can be formulated. In particular, our result implies that the
adiabatic theorem holds also for eigenvalues embedded in the continuous
spectrum. If there is information on the H\"older continuity of the
spectral measure, then one can also estimate the rate at which the
adiabatic limit is approached.