IOSR Journal of Applied Physics

Dynamics of Twointeracting Electronsinthree-Dimensional Lattice

Edison A. Enaibe

Published Jan 1, 2013• 0 citations

Abstract

The physical property of strongly correlated electrons on a three-dimensional (3D) 3 x 3 x 3 cluster of the simple cubic lattice is here presented.In the work we developed the unit step Hamiltonian as a solution to the single band Hubbard Hamiltonian for the case of two electrons interaction in a finite three dimensional lattice.The approximation to the Hubbard Hamiltonian study is actually necessary because of the strong limitation and difficulty pose by the Hubbard Hamiltonian as we move away from finite -size lattices to larger N -dimensional lattices.Thus this work has provided a means of overcoming the finite -size lattice defects as we pass on to a higher dimension.We have shown in this study, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.This study reveals that when the Coulomb interaction is zero, that is, for free electron system (non-interacting), thevariational parameters which describe the probability distribution of lattice electron system is the same.The spectra intensity for on-site electrons is zero for all values of the interaction strength.

DOI: 10.9790/4861-0427584

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