标题： 绝热定理与能隙条件无关 显示英文标题

标题： Adiabatic Theorem without a Gap Condition

摘要： 我们证明了量子演化下的绝热定理，而无需传统的能隙条件。 这个绝热定理所需要的仅仅是（分段）二阶可微的有限维谱投影。 该结果表明，绝热定理适用于量化辐射场中原子的基态。 我们所证明的一般性结果并未提供绝热极限接近的速度信息。 通过额外的谱信息，也可以估算出这一速度。 显示英文摘要

摘要： 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.