The properties of Bose-Einstein-condensed systems of hard spheres at high density are studied by taking into account higher-order corrections beyond the Hartree-Fock-Bogoliubov approximation. Based on a diagrammatic technique of the perturbation expansion starting from the Bogoliubov approximation, we show that the effective interactions separate into two distinct parts: the screened and condensate-mediated interactions. The latter is described by the exchange of virtual quasiparticles between noncondensate bosons via the Bose-Einstein condensate and is attractive for small energy transfer. We calculate the condensation temperature, excitation spectrum, and condensate density in the whole region of the gas parameter. It is shown that the condensate temperature decreases compared to that of an ideal Bose gas due to hard-sphere interactions. We find that the condensate-mediated attraction between noncondensate bosons leads to an enhancement of the anomalous self-energy and, as a consequence, to the emergence of a roton minimum in the excitation spectrum and to the strong suppression of the condensate fraction in the region of high density.The properties of Bose-Einstein-condensed systems of hard spheres at high density are studied by taking into account higher-order corrections beyond the Hartree-Fock-Bogoliubov approximation. Based on a diagrammatic technique of the perturbation expansion starting from the Bogoliubov approximation, we show that the effective interactions separate into two distinct parts: the screened and condensate-mediated interactions. The latter is described by the exchange of virtual quasiparticles between noncondensate bosons via the Bose-Einstein condensate and is attractive for small energy transfer. We calculate the condensation temperature, excitation spectrum, and condensate density in the whole region of the gas parameter. It is shown that the condensate temperature decreases compared to that of an ideal Bose gas due to hard-sphere interactions. We find that the condensate-mediated attraction between noncondensate bosons leads to an enhancement of the anomalous self-energy and, as a consequence, to the emergence of a roton minimum in the excitation spectrum and to the strong suppression of the condensate fraction in the region of high density.

Physical Review AMay 22, 20126 citations

Path-integral approach to bose condensation

Sivinee Sawatdiaree, Virulh Sa-yakanit

The excitation spectrum of the interacting Bose gas has two branches. The first branch was dominated in the low momentum area and high density of the ground state particles and the second one was dominated in the high momentum area and was existed in the density of the ground state particles which lower than the existed density of the ground state particles of the first branch. The functional integrals method was used. The Hamiltonian was introduced in form of the combination of field operators which was divided into two parts; ground state particles and exicted particles were described respectively the action and partition function were calculated and were introduced partition function poles which were defined as excitation spectrum. According to the definition of excitation energy of ground was equal to zero, parameters were calculated and devided both forms of Bose excitation spectrums in phase space. The interaction between boson particles in the system was replaced by our ansatz interaction. Its behaviour was like the Lennard-Jones potential. The ansatz interaction was mentioned in configuration space was varied with [e -alphar/(betar)2 - e -alphar/(betar)] by assigning α, β as unity with the inversion unit of length.The excitation spectrum of the interacting Bose gas has two branches. The first branch was dominated in the low momentum area and high density of the ground state particles and the second one was dominated in the high momentum area and was existed in the density of the ground state particles which lower than the existed density of the ground state particles of the first branch. The functional integrals method was used. The Hamiltonian was introduced in form of the combination of field operators which was divided into two parts; ground state particles and exicted particles were described respectively the action and partition function were calculated and were introduced partition function poles which were defined as excitation spectrum. According to the definition of excitation energy of ground was equal to zero, parameters were calculated and devided both forms of Bose excitation spectrums in phase space. The interaction between boson particles in the system was replaced by our ansatz interaction. Its behaviour was like the Lennard-Jones potential. The ansatz interaction was mentioned in configuration space was varied with [e -alphar/(betar)2 - e -alphar/(betar)] by assigning α, β as unity with the inversion unit of length.

Jan 1, 19960 citations

Excitation spectrum and structure factor for interacting bosons

Kapil M. Khanna, S. Chauba Singh, O. P. Sinha

Physica B+CAug 1, 19820 citations

Excitation Spectrum in an Ensemble of Hubbard Bosons

Valerii Vladimirovich Val'kov

An approach that makes it possible to correctly derive equations describing the Bose–Einstein condensation and the spectrum of elementary excitations in the ensemble of Hubbard bosons in the strong correlation regime $(U \gg {\text{|}}{{t}_{{fm}}}{\text{|}})$ has been developed in the atomic representation using the Dyson method with the introduced indefinite metric. The kinematic Dyson interaction caused by the properties of the commutation relations of dynamic variables plays an important role in such a system. An effective Hamiltonian has been obtained using the operator form of perturbation theory at finite U values. It has been shown that the properties of the ensemble of Hubbard bosons have been determined by the kinematic interaction, correlated hopping, and the attraction between Hubbard bosons. Numerical calculations have demonstrated the effect of these interactions on the characteristics of the energy spectrum of excitations of the ensemble of Hubbard bosons and on the dependence of the density of condensate particles on the density of bosons in the system.An approach that makes it possible to correctly derive equations describing the Bose–Einstein condensation and the spectrum of elementary excitations in the ensemble of Hubbard bosons in the strong correlation regime $$(U \gg {\text{|}}{{t}_{{fm}}}{\text{|}})$$ has been developed in the atomic representation using the Dyson method with the introduced indefinite metric. The kinematic Dyson interaction caused by the properties of the commutation relations of dynamic variables plays an important role in such a system. An effective Hamiltonian has been obtained using the operator form of perturbation theory at finite U values. It has been shown that the properties of the ensemble of Hubbard bosons have been determined by the kinematic interaction, correlated hopping, and the attraction between Hubbard bosons. Numerical calculations have demonstrated the effect of these interactions on the characteristics of the energy spectrum of excitations of the ensemble of Hubbard bosons and on the dependence of the density of condensate particles on the density of bosons in the system.

Journal of Experimental and Theoretical Physics LettersDec 1, 20220 citations

The Excitation Spectrum for Weakly Interacting Bosons

Robert Seiringer

arXiv:1008.5349Communications in Mathematical PhysicsMay 13, 2011112 citations

(U \gg {\text{|}}{{t}_{{fm}}}{\text{|}})

has been developed in the atomic representation using the Dyson method with the introduced indefinite metric. The kinematic Dyson interaction caused by the properties of the commutation relations of dynamic variables plays an important role in such a system. An effective Hamiltonian has been obtained using the operator form of perturbation theory at finite U values. It has been shown that the properties of the ensemble of Hubbard bosons have been determined by the kinematic interaction, correlated hopping, and the attraction between Hubbard bosons. Numerical calculations have demonstrated the effect of these interactions on the characteristics of the energy spectrum of excitations of the ensemble of Hubbard bosons and on the dependence of the density of condensate particles on the density of bosons in the system.