In the first paper of this series, the master-graph formulation of the Lee-Yang quantum statistical theory for a degenerate Bose system was derived. In the present paper, this entire theory is transformed from a free-particle description to a quasiparticle description by means of a $\ensuremath{\Lambda}$ transformation. This transformation leaves the master-graph formulation of the theory essentially unchanged, while at the same time introducing the quasiparticle energy-momentum relation and the quasiparticle interaction function into the theory. The transformation is motivated by a study of the very low-temperature behavior of the fundamental integral equation of the theory. An interesting feature of the transformed theory is that it contains two quasiparticle energy-momentum relations, ${\ensuremath{\epsilon}}_{+}(k)$ and ${\ensuremath{\epsilon}}_{\ensuremath{-}}(k)$. The understanding of this result is not achieved in this paper, although the possibility of a double quasiparticle spectrum has previously been suggested by Lieb.In the first paper of this series, the master-graph formulation of the Lee-Yang quantum statistical theory for a degenerate Bose system was derived. In the present paper, this entire theory is transformed from a free-particle description to a quasiparticle description by means of a $\ensuremath{\Lambda}$ transformation. This transformation leaves the master-graph formulation of the theory essentially unchanged, while at the same time introducing the quasiparticle energy-momentum relation and the quasiparticle interaction function into the theory. The transformation is motivated by a study of the very low-temperature behavior of the fundamental integral equation of the theory. An interesting feature of the transformed theory is that it contains two quasiparticle energy-momentum relations, ${\ensuremath{\epsilon}}_{+}(k)$ and ${\ensuremath{\epsilon}}_{\ensuremath{-}}(k)$. The understanding of this result is not achieved in this paper, although the possibility of a double quasiparticle spectrum has previously been suggested by Lieb.

Physical ReviewAug 17, 19647 citations

Quasiparticle Approximations in an Exactly Solvable Model

Y. Takahashi

Progress of Theoretical PhysicsJul 1, 19750 citations

Slater Determinants and Quasiparticle Vacuum States Constructed from a Finite Number of Fermion States

A. M. Navon, A. Bose

A theoretical study of single-particle transformations, quasiparticle transformations, Slater determinants, and quasiparticle vacuum states is made for a given finite number of single-fermion states. The usual unitary single-particle or quasiparticle transformations are generalized. The new transformations are the most general transformations which transform Slater determinants into Slater determinants or quasiparticle vacuum states into quasiparticle vacuum states, and they contain as particular cases Thouless's nonunitary transformation. It is shown that several Brillouin theorems used in Hartree-Fock and Hartree-Bogolubov variation theories follow from the form of the continuous variations which can be performed in the space of Slater determinants and in the space of quasiparticle vacuum states.A theoretical study of single-particle transformations, quasiparticle transformations, Slater determinants, and quasiparticle vacuum states is made for a given finite number of single-fermion states. The usual unitary single-particle or quasiparticle transformations are generalized. The new transformations are the most general transformations which transform Slater determinants into Slater determinants or quasiparticle vacuum states into quasiparticle vacuum states, and they contain as particular cases Thouless's nonunitary transformation. It is shown that several Brillouin theorems used in Hartree-Fock and Hartree-Bogolubov variation theories follow from the form of the continuous variations which can be performed in the space of Slater determinants and in the space of quasiparticle vacuum states.

Physical ReviewJan 20, 19695 citations

Hartree-Fock-Bogoliubov theory without quasiparticle vacua

George Rosensteel

Hartree-Fock-Bogoliubov (HFB) theory is generalized by eliminating the restriction to quasiparticle vacuum states. However, the fundamental HFB transformation to quasiparticles is retained. The theory is formulated in terms of the quasiparticle density matrix $R$ , but, in contrast to conventional HFB, there is no restriction to vacuum densities ${R}^{2}=R$ .Hartree-Fock-Bogoliubov (HFB) theory is generalized by eliminating the restriction to quasiparticle vacuum states. However, the fundamental HFB transformation to quasiparticles is retained. The theory is formulated in terms of the quasiparticle density matrix $R$, but, in contrast to conventional HFB, there is no restriction to vacuum densities ${R}^{2}=R$.

Physical Review AJun 1, 198118 citations

On the description of quasiparticles my Green's functions

Vyacheslav I. Yukalov

Theoretical and Mathematical PhysicsDec 1, 197315 citations

R

, but, in contrast to conventional HFB, there is no restriction to vacuum densities

{R}^{2}=R