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TMF, 1977, Volume 32, Number 2, Pages 247–261 (Mi tmf3153)  

This article is cited in 9 scientific papers (total in 9 papers)

Irreducible cluster expansion for the logarithm of the $s$-particle density matrix of a many-boson system

I. A. Vakarchuk


Abstract: Irreducible cluster expansion for the logarithm of the $s$-particle density matrix is obtained by means of integrating the variational wave functions which take into account the pair correlations. The integration is performed with the aid of the (proposed earlier) method of integration over the collective variables of $(N - s)$ particles. The relationship between the number of particles in the Bose-condensate and the structural functions of the system is established and the estimate of the number of particles for the liquid He$^4$ is found. In the model systems, the formulas obtained are exact ones up to the second order in the nonideality parameter and are valid in the case of the strong nonideality as well. The calculation of the dependence of the ground state energy of one-dimensional Bose-gas on the nonideality parameter $\gamma$ is performed. The results of the calculation are in the agreement with the exact solution in all the range of the parameter $\gamma$.

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English version:
Theoretical and Mathematical Physics, 1977, 32:2, 720–730

Bibliographic databases:

Received: 26.10.1976

Citation: I. A. Vakarchuk, “Irreducible cluster expansion for the logarithm of the $s$-particle density matrix of a many-boson system”, TMF, 32:2 (1977), 247–261; Theoret. and Math. Phys., 32:2 (1977), 720–730

Citation in format AMSBIB
\Bibitem{Vak77}
\by I.~A.~Vakarchuk
\paper Irreducible cluster expansion for the logarithm of the $s$-particle density matrix of a many-boson system
\jour TMF
\yr 1977
\vol 32
\issue 2
\pages 247--261
\mathnet{http://mi.mathnet.ru/tmf3153}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=449365}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 32
\issue 2
\pages 720--730
\crossref{https://doi.org/10.1007/BF01036335}


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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. I. A. Vakarchuk, “Microscopic theory of the $\lambda$-transition in liquid $\mathrm{He}^4$. I”, Theoret. and Math. Phys., 36:1 (1978), 639–648  mathnet  crossref
    2. V. I. Yukalov, “Bose condensation into a state with finite momentum”, Theoret. and Math. Phys., 37:3 (1978), 1093–1101  mathnet  crossref
    3. I. A. Vakarchuk, I. R. Yukhnovskii, “Microscopic theory of the energy spectrum of liquid HeII”, Theoret. and Math. Phys., 42:1 (1980), 73–80  mathnet  crossref  isi
    4. I. A. Vakarchuk, “Bose condensate in liquid $\textrm{He}^4$”, Theoret. and Math. Phys., 65:2 (1985), 1164–1171  mathnet  crossref  mathscinet  isi
    5. G. O. Balabanyan, “Construction of theory of a binary mixture of nonideal Bose gases (or liquids) by the method of collective variables I. Wave function and ground-state energy, excitation spectrum, correlation functions, thermodynamics of the system at $T=0$”, Theoret. and Math. Phys., 66:1 (1986), 81–97  mathnet  crossref  mathscinet  isi
    6. 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  mathnet  crossref  isi
    7. 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  mathnet  crossref  isi
    8. I. A. Vakarchuk, “Density matrices of superfluid helium-4. I”, Theoret. and Math. Phys., 80:3 (1989), 983–991  mathnet  crossref  isi
    9. I. A. Vakarchuk, “Density matrices of superfluid helium-4. II”, Theoret. and Math. Phys., 82:3 (1990), 308–316  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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