DOI: https://doi.org/10.30970/jps.01.156
NEW RESULTS FOR THE DISTRIBUTION FUNCTIONS OF MANY-PARTICLE QUANTUM SYSTEMS
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Journal of Physical Studies 1(2), 156–168 (1997)
DOI: https://doi.org/10.30970/jps.01.156 NEW RESULTS FOR THE DISTRIBUTION FUNCTIONS OF MANY-PARTICLE QUANTUM SYSTEMS |
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I. O. Vakarchuk
Ivan Franko Lviv State University, Chair of Theoretical Physics
12 Drahomanov Str., Lviv UA-290005, Ukraine
A method of calculation of the density matrices for a system of identical particles is suggested. The method is based on a partial summation of the series which appear during the expansion of a full $N$-particle density matrix of ideal quantum gas with respect to the lower matrices of the order $N-s$. The expressions for the one- and two-particle density matrices of many boson system were found in the explicit form. For the low temperatures they turn into the the well-known expressions of the theory of the ground state of Bose liquids. As for the ideal gas there arises a point of nonanalliticity of these expressions which is connected with the Bose-Einstein condensation. The obtained results may be easily generalized for the case of many-fermion systems, which allows to study not only the properties of the superfluid $^4$He but also such systems as electron gas and liquid $^3$He.