On the ground state energy of the inhomogeneous Bose gas
Within the self-consistent Hartree–Fock approximation, an explicit in this approximation expression for the ground state energy of inhomogeneous Bose gas is derived as a functional of the inhomogeneous density of the Bose–Einstein condensate. The results obtained are based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose–Einstein condensate. This makes it possible to avoid the use of anomalous averages. The explicit form of the kinetic energy, which differs from one in the Gross–Pitaevski approach, is found. The obtained form of kinetic energy is valid beyond the Hartree–Fock approximation and can be applied for arbitrary strong interparticle interaction.
KeywordsBose condensation elementary excitations single-particle Green function density-density Green function thermodynamic energy
The authors are grateful to A. G. Khrapak, A. A. Rukhadze, P. P. J. M. Schram and A. G. Zagorodny for helpful discussions. This study was supported by the Russian Science Foundation (Project No. 14-19-01492).
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