We discuss a variational approach to collective excitations in a boson formalism based on quasiparticles. Bosons are defined in correspondence with pairs of quasiparticles and boson images of fermion operators are constructed by means of a mapping procedure of Marumori-type. Phonons of the type used within the random phase approximation (RPA) are introduced as Bogoliubov transformations of these bosons. The variables entering into the definition of these phonons as well as of the quasiparticle operators are fixed simultaneously by minimizing the expectation value of the boson Hamiltonian in the vacuum of the phonons. The approach is tested within an exactly solvable two-level model which is characterized by a pairing Hamiltonian. A quite good agreement is found for the energies of the ground state and of the first ${0}^{+}$ excited state. The comparison with the Bardeen-Cooper-Schrieffer method and the quasiparticle RPA as well as with some recent self-consistent RPA-type approaches is discussed.We discuss a variational approach to collective excitations in a boson formalism based on quasiparticles. Bosons are defined in correspondence with pairs of quasiparticles and boson images of fermion operators are constructed by means of a mapping procedure of Marumori-type. Phonons of the type used within the random phase approximation (RPA) are introduced as Bogoliubov transformations of these bosons. The variables entering into the definition of these phonons as well as of the quasiparticle operators are fixed simultaneously by minimizing the expectation value of the boson Hamiltonian in the vacuum of the phonons. The approach is tested within an exactly solvable two-level model which is characterized by a pairing Hamiltonian. A quite good agreement is found for the energies of the ground state and of the first ${0}^{+}$ excited state. The comparison with the Bardeen-Cooper-Schrieffer method and the quasiparticle RPA as well as with some recent self-consistent RPA-type approaches is discussed.

Physical Review CMar 1, 199921 citations

Dynamic electron -phonon interactions in one-dimensional models

Rahul P. Hardikar

Jan 1, 20070 citations

Solvable many-level pairing model in a boson formalism

D. Gambacurta, Michelangelo Sambataro, F. Catara

We analyze an exactly solvable many-level pairing model (the picket-fence model) in a boson formalism. By making use of a Marumori-type mapping procedure, we construct a boson image of the model Hamiltonian. Only two- and four-boson operators are included in the boson expansion. We show that the physical spectrum of this Hamiltonian coincides with the exact one, and, in particular, we recover Richardson's equations. We apply this boson formalism to search for possible extensions of the random-phase approximation (RPA). We construct renormalized RPA-type equations in correspondence with different expansions of the boson operators. We discuss two extensions of the RPA and test them by comparing their predictions with the exact results and with those obtained within the RPA and the self-consistent RPA.We analyze an exactly solvable many-level pairing model (the picket-fence model) in a boson formalism. By making use of a Marumori-type mapping procedure, we construct a boson image of the model Hamiltonian. Only two- and four-boson operators are included in the boson expansion. We show that the physical spectrum of this Hamiltonian coincides with the exact one, and, in particular, we recover Richardson's equations. We apply this boson formalism to search for possible extensions of the random-phase approximation (RPA). We construct renormalized RPA-type equations in correspondence with different expansions of the boson operators. We discuss two extensions of the RPA and test them by comparing their predictions with the exact results and with those obtained within the RPA and the self-consistent RPA.

Physical Review CJan 26, 20067 citations

Phonons from a many-body viewpoint

R. D. Mattuck

Annals of PhysicsApr 1, 196414 citations

Phonons from a many-body viewpoint

R. D. Mattuck

Annals of PhysicsFeb 1, 19640 citations

{0}^{+}

excited state. The comparison with the Bardeen-Cooper-Schrieffer method and the quasiparticle RPA as well as with some recent self-consistent RPA-type approaches is discussed.