Adiabatic Theorem without a Gap Condition
Mathematical Physics
2009-10-31 v4 math.MP
Spectral Theory
Atomic Physics
Quantum Physics
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.
Keywords
Cite
@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}
}
Comments
23 pages, revised and extended with 4 figures, to appear in Comm. Math. Phys