We present an operator-algebraic approach to derive the low-lying quasidegenerate spectrum of weakly interacting trapped N bosons with total angular momentum $\ensuremath{\Elzxh}L$ for the case of $L/N\ensuremath{\ll}1.$ We demonstrate that the lowest-lying excitation spectrum is given by ${27gn}_{3}{(n}_{3}\ensuremath{-}1)/34,$ where g is the strength of the repulsive contact interaction and ${n}_{3}$ is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.We present an operator-algebraic approach to derive the low-lying quasidegenerate spectrum of weakly interacting trapped N bosons with total angular momentum $\ensuremath{\Elzxh}L$ for the case of $L/N\ensuremath{\ll}1.$ We demonstrate that the lowest-lying excitation spectrum is given by ${27gn}_{3}{(n}_{3}\ensuremath{-}1)/34,$ where g is the strength of the repulsive contact interaction and ${n}_{3}$ is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.

arXiv:cond-mat/0012458Physical Review ANov 15, 20016 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

{n}_{3}

is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.

(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.