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Journal of Physical Studies 13(3), Article 3004 [28 pages] (2009)
DOI: https://doi.org/10.30970/jps.13.3004 DENSITY MATRIX OF THE MANY-BOSON SYSTEM WITH THE CONSIDERATION OF THREE- AND FOUR-PARTICLE DIRECT CORRELATIONSI. O. Vakarchuk, O. I. Hryhorchak
Chair for Theoretical Physics, Ivan Franko National
University of Lviv, |
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In this article the density matrix of the interacting Bose-particles with three- and four-particle direct correlations taken into account is found in the coordinate representation for a wide temperature domain from the first principles. In the low temperature limit the obtained expression for the density matrix agrees with the already known one [I. O. Vakarchuk, I. R. Yukhnovskii, Theor. Math. Phys {\bf 40}, 626 (1979)] and has the form of the product of the ground-state wave functions with three- and four-particle direct correlations taken into account and the factor $e^{-E_0/T}$, where $T$ is the temperature of the system, $E_0$ is the ground state energy in the approximation of ‟two sums over the wave vector”. For high temperatures in the quasi-classical limit the obtained expression is equal to the product of the partition function of classical ideal gas and the Boltzmann factor. The results of this work can be applied to the calculation of the thermodynamic and structure functions of liquid $^4$He in order to check the theoretical and experimental results quantitavely, especially in the $λ$-transition region.
PACS number(s): 05.30.Jp, 67.20.+k, 67.40.-w, 67.40.Db, 67.40.Kh