### 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 language | English |
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Pages (from-to) | 314-327 |

Number of pages | 14 |

Journal | Journal of Mathematical Chemistry |

Volume | 43 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2008 |

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### 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.

Research output: Contribution to journal › Article

*Journal of Mathematical Chemistry*, vol. 43, no. 1, pp. 314-327. https://doi.org/10.1007/s10910-006-9197-3

}

TY - JOUR

T1 - Iterative solution of Bloch-type equations

T2 - Stability conditions and chaotic behavior

AU - Szakács, Péter

AU - Surján, P.

PY - 2008/1

Y1 - 2008/1

N2 - 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.

AB - 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.

KW - Bloch equation

KW - Chaos

KW - Density matrix

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=37549009113&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37549009113&partnerID=8YFLogxK

U2 - 10.1007/s10910-006-9197-3

DO - 10.1007/s10910-006-9197-3

M3 - Article

AN - SCOPUS:37549009113

VL - 43

SP - 314

EP - 327

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 1

ER -