Adiabatic Theorem without a Gap Condition

Details Adiabatic Theorem without a Gap Condition Adiabatic Theorem without a Gap Condition

1998-05-25

arxiv.org/abs/math-ph/9805022v4

Commun.Math.Phys. 203 (1999) 445-463

Physics

Mathematical Physics

23 pages, revised and extended with 4 figures, to appear in Comm. Math. Phys

Scientific paper

10.1007/s002200050620

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.

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