Adiabatic Theorem without a Gap Condition
数学物理
2009-10-31 v4 math.MP
谱理论
原子物理
量子物理
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.
引用
@article{arxiv.math-ph/9805022,
title = {Adiabatic Theorem without a Gap Condition},
author = {J. E. Avron and A. Elgart},
journal= {arXiv preprint arXiv:math-ph/9805022},
year = {2009}
}
备注
23 pages, revised and extended with 4 figures, to appear in Comm. Math. Phys