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Bifurcations; Hartree-Fock calculation; periodic solutions

The Hartree-Fock procedure is used to study the behaviour of the ground state of a system ofM spinless electrons distributed overN equivalent and equidistant sites (M ⩽N) as a function of the strength of the mutual repulsion between the electrons. Below a critical strength, all initial configurations are seen, after repeated iterations, to converge to a unique solution. Above this critical strength, in addition to the initial configurations which lead to a unique solution, there exist configurations which on repeated iterations give rise to stable two-period solutions. Although the number of independent stable two-period solutions depends on the coupling strength, for no value of the coupling are stable solutions of periodicity higher than two seen.

Arvinder Kaur¹ P K Srivastava¹ V S Varma¹

1. Department of Physics and Astrophysics, University of Delhi, Delhi - 110 007, India

Published

February 1989

Manuscript received

22 August 1988

Manuscript revised

6 December 1988