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

Péter Szakács, P. Surján

Research output: Contribution to journalArticle

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 2008

Fingerprint

Iterative Solution
Chaotic Behavior
Stability Condition
Electrons
Stiffness matrix
Exponent
Nonlinear equations
Electron
Wave Operator
Density Matrix
Iterative Procedure
First-order
Eigenvalue
Iteration

Keywords

  • Bloch equation
  • Chaos
  • Density matrix
  • Stability

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

Iterative solution of Bloch-type equations : Stability conditions and chaotic behavior. / Szakács, Péter; Surján, P.

In: Journal of Mathematical Chemistry, Vol. 43, No. 1, 01.2008, p. 314-327.

Research output: Contribution to journalArticle

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