Adjacency graphs and long-range interactions of atoms in quasi-degenerate states: Applied graph theory

C. M. Adhikari, V. Debierre, U. Jentschura

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We analyze, in general terms, the evolution of energy levels in quantum mechanics, as a function of a coupling parameter, and demonstrate the possibility of level crossings in systems described by irreducible matrices. In long-range interactions, the coupling parameter is the interatomic distance. We demonstrate the utility of adjacency matrices and adjacency graphs in the analysis of "hidden" symmetries of a problem; these allow us to break reducible matrices into irreducible subcomponents. A possible breakdown of the no-crossing theorem for higherdimensional irreducible matrices is indicated, and an application to the 2S-2S interaction in hydrogen is briefly described. The analysis of interatomic interactions in this system is important for further progress on optical measurements of the 2S hyperfine splitting.

Original languageEnglish
Title of host publicationExploring the World with the Laser
Subtitle of host publicationDedicated to Theodor Hänsch on his 75th Birthday
PublisherSpringer International Publishing
Pages159-174
Number of pages16
ISBN (Electronic)9783319643465
ISBN (Print)9783319643458
DOIs
Publication statusPublished - Jan 2 2018

ASJC Scopus subject areas

  • Chemistry(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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    Adhikari, C. M., Debierre, V., & Jentschura, U. (2018). Adjacency graphs and long-range interactions of atoms in quasi-degenerate states: Applied graph theory. In Exploring the World with the Laser: Dedicated to Theodor Hänsch on his 75th Birthday (pp. 159-174). Springer International Publishing. https://doi.org/10.1007/978-3-319-64346-5_11