Geometrical approach to two-level Hamiltonians

L. Carmel*, A. Mann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Two-level systems were shown to be fully described by a single function, known sometimes as the Stueck-elberg parameter. Using concepts from differential geometry, we give geometrical meaning to the Stueckelberg parameter and to other related quantities. As a result, a generalization of the Stueckelberg parameter is introduced, and a relation obtained between two-level systems 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 fundamental models, from which many other known models emerge as special cases. We present the detailed analysis of these models.

Original languageEnglish
Article number052113
Pages (from-to)521131-5211314
Number of pages4690184
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number5
StatePublished - May 2000
Externally publishedYes


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