Geometrical approach to two-level Hamiltonians - art. no. 052113

Two-level systems were shown to be fully described by a single function, kn own sometimes as the Stueckelberg parameter. Using concepts from differenti al geometry, we give geometrical meaning to the Stueckelberg parameter and to other related quantities. As a result, a generalization of the Stueckelb erg parameter is introduced, and a relation obtained between two-level syst ems and spatial one-dimensional curves in three-dimensional space. Previous authors used this Stueckelberg parameter to solve analytically several two -level models. We further develop this idea, and solve analytically three f undamental models, from which many other known models emerge as special cas es. We present the detailed analysis of these models.