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

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

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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
2. V. I. Yukalov, “Bose condensation into a state with finite momentum”, Theoret. and Math. Phys., 37:3 (1978), 1093–1101
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
4. I. A. Vakarchuk, “Bose condensate in liquid $\textrm{He}^4$”, Theoret. and Math. Phys., 65:2 (1985), 1164–1171
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
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
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
8. I. A. Vakarchuk, “Density matrices of superfluid helium-4. I”, Theoret. and Math. Phys., 80:3 (1989), 983–991
9. I. A. Vakarchuk, “Density matrices of superfluid helium-4. II”, Theoret. and Math. Phys., 82:3 (1990), 308–316
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