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Progress of Theoretical Physics

Theory of Bose-Einstein Condensation of an Imperfect Bose-Einstein Gas

Takeo Matsubara, Akira Morita, Namio Honda

Published Nov 1, 1956• 0 citations
Publisher

Abstract

In orde to clarify the behavior of the Bose-Einstein condensation, to which various investigations have been reported with results being in conflict with each other, the influence of binary collisions to the Bose-Einstein condensation is treated correctly. As the result, it is shown that the B-E condensation is of the third order, as in the case of an ideal Bose-Einstein gas model.

DOI
10.1143/ptp.16.447

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In orde to clarify the behavior of the Bose-Einstein condensation, to which various investigations have been reported with results being in conflict with each other, the influence of binary collisions to the Bose-Einstein condensation is treated correctly. As the result, it is shown that the B-E condensation is of the third order, as in the case of an ideal Bose-Einstein gas model.
We present a review of some published results concerning evolution of the notion of (conventional ) Bose-Einstein condensation (BEC) predicted in Ideal Bose-Gas (IBG) in 1925. The first step forward was the notion of the conventional generalised BEC à la van den Berg-Lewis-Pulé discovered in the IBG and later in certain models with interactions in 1980s. The next development was a discovery of non-conventional condensation of bosons that occurs only due to interaction. Finally we discuss an example of (non-ideal) the Weakly Imperfect Bose-Gas (WIBG), where the conventional and non-conventional condensates may coexist due to interaction.
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.
From a certain temperature on, the molecules “condense” without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there also some truth to it? Albert Einstein, Letter to Ehrenfest (Dec. 1924). Abraham Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein , Oxford University Press, New York (1982) Introduction For over 50 years the low-temperature liquid state of uncharged, spinless He 4 was the only system in which a Bose–Einstein (BE) condensation was considered experimentally realized. In that case, cold (<2.19K) liquid He 4 passes into an extraordinary phase of matter called a superfluid , in which the liquid's viscosity and entropy become zero. With advances in atomic cooling (to ≈ 10 –9 K) the number of Bose systems which demonstrably pass into a condensate has considerably increased. These include several isotopes of alkali gas atoms as well as fermionic atoms that pair into integerspin (boson) composites. Although an ideal Bose gas does exhibit a low-temperature critical instability, the ideal BE gas theory is not, on its own, able to describe the BE condensate wave state. In order for a theory of bosons to account for a condensate wave state, interactions between the bosons must be included. Nevertheless, considerable interesting physics is contained in the ideal Bose gas model.