Adiabatic Theorem without a Gap Condition

@misc{citeulike:1196739, abstract = {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.}, author = {Avron, J. E. and Elgart, A. }, citeulike-article-id = {1196739}, eprint = {math-ph/9805022}, keywords = {adiabatic}, month = {Apr}, posted-at = {2007-05-31 04:15:36}, priority = {3}, title = {Adiabatic Theorem without a Gap Condition}, url = {http://arxiv.org/abs/math-ph/9805022}, year = {1999} }

TY - ELEC ID - citeulike:1196739 L3 - citeulike-article-id:1196739 TI - Adiabatic Theorem without a Gap Condition N2 - 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. KW - adiabatic AU - Avron, JE AU - Elgart, A PY - 1999/Apr/19/ UR - http://arxiv.org/abs/math-ph/9805022 ER -