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NATO science for peace and security series. B, Physics and biophysics

An Approximating Hamiltonian Method In The Theory of Imperfect Bose Gases

N. N. Bogolyubov, Дмитрий Петрович Санкович

Published Oct 7, 2010• 0 citations
Publisher
DOI
10.1007/978-94-007-0044-4_17

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It has been shown that Mayer's theory of imperfect gases can be handled approximately as a problem in association in which the actual gas is replaced by a mixture of ideal gases consisting of clusters of all sizes and between which dissociative equilibrium exists. Kahn and Uhlenbeck have shown how Mayer's theory can be generalized to apply to quantum degenerate gases. The purpose of the present paper is to examine the clustering approximation to such a theory of the quantum degenerate Bose-Einstein gas. The symmetrized wave functions for the clustering assembly are set up and the partition function evaluated for all ways of clustering. Equations of state are deduced that include condensation into the liquid phase as a clustering avalanche at the saturation pressure. It is found that clustering has the effect of lowering the lambda-temperature due to statistical degeneracy right down to the saturated vapor line, so that the lambda-transition is entirely inhibited from the gas phase.
The exactness of the Bogoliubov approximation is discussed from the point of view of the condensation properties of the Bose gas. For the imperfect Bose gas, the authors find that the approximation yields the correct condensate density when the thermodynamic limit is taken by isotropic dilation; this is not the case in general for other ways of going to the infinite volume limit. They also prove the existence of Bose-Einstein condensation for a class of Bose gases with weak interactions and an energy gap.