Exponentiation of certain Matrices related to the Four Level System by use of the Magic Matrix
Quantum Physics
2008-02-29 v3 Mathematical Physics
math.MP
Abstract
In this paper we show how to calculate explicitly the exponential of certain matrices, which are evolution operators governing the interaction of the four level system of atoms and the radiation, etc. We present a consistent method in terms of the magic matrix by Makhlin. As a closely related subject, we derive a closed form expression of the Baker-Campbell-Hausdorff formula for a class of matrices in SU(4), by use of the method developed by the present authors in quant-ph/0610009.
Keywords
Cite
@article{arxiv.quant-ph/0701092,
title = {Exponentiation of certain Matrices related to the Four Level System by use of the Magic Matrix},
author = {Kazuyuki Fujii},
journal= {arXiv preprint arXiv:quant-ph/0701092},
year = {2008}
}
Comments
Latex ; 13 pages ; 2 figures ; substantial changes (including the title) made. To appear in Yokohama Mathematical Journal (2007)