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 TMF, 1985, Volume 65, Number 2, Pages 285–295 (Mi tmf5101)

Bose condensate in liquid $\textrm{He}^4$

I. A. Vakarchuk

Abstract: Expressions for the single-particle density matrix of a Bose fluid and the amount of Bose condensate are found in terms of the liquid structure factor. A self-consistent perturbation theory with respect to the exactly solvable hard-spheres model is formulated for the logarithm of the relative number of atoms of the Bose condensate. The packing parameter for the hard spheres is found from the compensation equation for the first-order correction. This has made itpossible to take into account correctly the contribution of pair correlations between atoms of the liquid to the dynamical “erosion”of the Bose condensate. The Bogolyubov–Zubarev expression for the ground-state energy of a many-boson system is used to calculate the contribution of the three- and fourparticle correlations to the density matrix and estimate the contribution numerically. The results of the theory are used to calculate the filling of the Bose condensate in the ground state of liquid $\textrm{He}^4$ as a function of the liquid density.

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English version:
Theoretical and Mathematical Physics, 1985, 65:2, 1164–1171

Bibliographic databases:

Citation: I. A. Vakarchuk, “Bose condensate in liquid $\textrm{He}^4$”, TMF, 65:2 (1985), 285–295; Theoret. and Math. Phys., 65:2 (1985), 1164–1171

Citation in format AMSBIB
\Bibitem{Vak85} \by I.~A.~Vakarchuk \paper Bose condensate in liquid $\textrm{He}^4$ \jour TMF \yr 1985 \vol 65 \issue 2 \pages 285--295 \mathnet{http://mi.mathnet.ru/tmf5101} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=823667} \transl \jour Theoret. and Math. Phys. \yr 1985 \vol 65 \issue 2 \pages 1164--1171 \crossref{https://doi.org/10.1007/BF01017941} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985C929000012} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. O. Balabanyan, “Construction of theory of a binary mixture of nonideal bose gases (or liquids) by the method of collective variables. II. The $s$-particle density matrices at $T=0$. Variational calculation of the ground-state energy and density-density correlation functions”, Theoret. and Math. Phys., 71:1 (1987), 418–428
2. I. A. Vakarchuk, P. A. Glushak, “Free energy of a many-boson system at low temperatures”, Theoret. and Math. Phys., 75:1 (1988), 399–408
3. I. A. Vakarchuk, “Density matrices of superfluid helium-4. I”, Theoret. and Math. Phys., 80:3 (1989), 983–991
4. I. A. Vakarchuk, “Density matrices of superfluid helium-4. II”, Theoret. and Math. Phys., 82:3 (1990), 308–316
5. I. A. Vakarchuk, “One-particle density matrix of liquid $^4He$”, Theoret. and Math. Phys., 154:1 (2008), 6–25
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