1998/05/31 by J. E. Avron, A. Elgart · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.SP #physics.atom-ph #quant-ph
paper · pdf · doi:10.1007/s002200050620
published as Commun.Math.Phys. 203 (1999) 445-463 · 23 pages, revised and extended with 4 figures, to appear in Comm. Math. Phys
arxiv created 1999/04/19 · arxiv updated 2009/11/30
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate.