Iterative solution of Bloch-type equations: Stability conditions and chaotic behavior

Péter Szakács, Péter R. Surján

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5 Citations (Scopus)

Abstract

Two different form of nonperturbative Bloch-type equations are studied: one for the wave operator of the N-electron Schrödinger equation, another one for obtaining first-order density matrix P in one-electron theories (Hartree-Fock or Kohn-Sham). In both cases, we investigate the possibility of an iterative solution of the nonlinear Bloch equation. To have a closer view on convergence features, we determine the stability matrix of the iterative procedures and determine the Ljapunov exponents from its eigenvalues. For some of the cases when not every exponents are negative, chaotic solutions can be identified, which should of course be carefully avoided in practical iterations.

Original languageEnglish
Pages (from-to)314-327
Number of pages14
JournalJournal of Mathematical Chemistry
Volume43
Issue number1
DOIs
Publication statusPublished - Jan 1 2008

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Keywords

  • Bloch equation
  • Chaos
  • Density matrix
  • Stability

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

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