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Zeitschrift für Physik B Condensed Matter

A rearrangement of the Feenberg perturbation formula and elementary excitation interactions in bose fluids

Srećko Kilić, C. E. Campbell

Published Mar 1, 1996• 3 citations
Publisher
DOI
10.1007/s002570050188

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We used rearranged Feenberg perturbation formula which was adopted to describe the states with two quasiparticles of the momenta ħk1→ and ħk2 →. It was noticed that two “diagrams of states” of order N° (N is the number of the particles in the system) in the fourth order perturbation term contained the interaction between particles out of the condensate. The interaction energy described by these diagrams was calculated for the potential V q = V ( -q2 + g2), ), which had the main features of the real potential between two helium atoms, and for antiparallel momenta ħk1→ = ħk2 →. It was shown that the spectrum depended on the density strongly and in particular that the interaction changed its sign and became repulsive with the increase of density. Owing to the form of the interaction diagrams, Bogoliubov summing was possible. After numerical integration we found that this approximation had a significant influence on the spectrum, although qualitative picture of the interaction was unchanged.

•Jan 1, 1990•0 citations
Abstract Brillouin‐Wigner (BW) perturbation formulae can be rearranged into a form first proposed by Feenberg. Feenberg's perturbation formulae also follow from a variational principle. They are successfully tested at two typical problems, for which ordinary perturbation techniques completely fail. The first is to find conditions for the bosonization of the Tomonaga model perturbatively. The second is to clarify whether non‐Fermi liquid behavior of the momentum distribution function of the Luttinger model can be achieved perturbatively.
We used rearranged Feenberg perturbation formula which was adopted to describe the states with two quasiparticles of the momenta ħk1→ and ħk2 →. It was noticed that two “diagrams of states” of order N° (N is the number of the particles in the system) in the fourth order perturbation term contained the interaction between particles out of the condensate. The interaction energy described by these diagrams was calculated for the potential V q = V ( -q2 + g2), ), which had the main features of the real potential between two helium atoms, and for antiparallel momenta ħk1→ = ħk2 →. It was shown that the spectrum depended on the density strongly and in particular that the interaction changed its sign and became repulsive with the increase of density. Owing to the form of the interaction diagrams, Bogoliubov summing was possible. After numerical integration we found that this approximation had a significant influence on the spectrum, although qualitative picture of the interaction was unchanged.