On the different types of states of a one dimensional system of electrons in the Hartree-Fock method

Based on a theoretical model proposed for an organic bipartite lozenge ferrimagnetic chain, the spin configuration of π electrons and the dimerization are investigated. With the Hartree–Fock approximation, the strong electron–phonon coupling and the electron–electron interaction in the one-dimensional system are taken into account self-consistently. It is shown that around the middle of the chain appears a π electron spin polarization cloud with alternation of sign and amplitude of the spin density extending over a certain distance, which extends all over the chain with no decay when the e–e interaction is larger than a critical value. In the stable ferrimagnetic state, the antiferromagnetic exchange interaction between electrons at site A and site B along the chain will become very strong, and almost zero dimerization happens for the chain.

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Electronic-phase transition associated with instability of the Hartree-Fock solution of infinite one-dimensional system

International Journal of Quantum Chemistry ◽

10.1002/qua.560420106 ◽

1992 ◽

Vol 42 (1) ◽

pp. 45-54 ◽

Cited By ~ 5

Author(s):

Kazuyoshi Tanaka ◽

Hiromi Kobayashi ◽

Mayumi Okada ◽

Masahiro Kobashi ◽

Tokio Yamabe

Keyword(s):

Phase Transition ◽

Dimensional System ◽

One Dimensional ◽

Hartree Fock ◽

Electronic Phase

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ANISOTROPY IN THE COMPRESSIBLE QUANTUM HALL STATE

International Journal of Modern Physics B ◽

10.1142/s0217979201005854 ◽

2001 ◽

Vol 15 (10n11) ◽

pp. 1373-1376

Author(s):

NOBUKI MAEDA

Keyword(s):

Mean Field Theory ◽

Density Wave ◽

Quantum Hall ◽

Mean Field ◽

Dimensional System ◽

Von Neumann ◽

One Dimensional ◽

Hartree Fock ◽

Fermion Systems ◽

Lattice Fermion

Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around ν=l+1/2 in the quantum Hall system. The Hartree-Fock energy of the unidirectional charge density wave (UCDW) are calculated self-consistently. In these states the UCDW seems to be the most plausible state. We show that the UCDW is regarded as a collection of the one-dimensional lattice fermion systems which extend to the uniform direction. The kinetic energy of this one-dimensional system is induced from the Coulomb interaction term and the self-consistent Fermi surface is obtained.

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Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19980761 ◽

1998 ◽

Vol 63 (6) ◽

pp. 761-769 ◽

Cited By ~ 1

Author(s):

Roland Krämer ◽

Arno F. Münster

Keyword(s):

Reaction Diffusion ◽

Dominant Mode ◽

Reaction Diffusion System ◽

Diffusion System ◽

Local Perturbation ◽

Dimensional System ◽

One Dimensional ◽

Brusselator Model ◽

The One ◽

Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

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