Microscopic Theory of a Bose Fluid Below the Bose - Condensation Temperature .

C. J. Pethick, H. Smith

Franz Mohling, Indira Ramarao, Dion W. J. Shea

A simplified derivation of the master-graph formulation of the quantum-statistical theory of an interacting quantum fluid is presented. A complete analysis of the self-energy structures arising from both particle statistics and particle interactions simplifies the master-graph expressions for the thermodynamic properties of the fluid. The $x$-ensemble formulation of Lee and Yang is used to treat the degenerate Bose fluid below its Bose-Einstein condensation temperature. The results for a Bose fluid above its Bose-Einstein condensation temperature and for a Fermi fluid are obtained as special cases.

T. R. Kirkpatrick, J. R. Dorfman

The Landau-Khalatnikov two-fluid hydrodynamic equations are derived for a dilute, weakly interacting, condensed Bose gas on the basis of a microscopic theory. Explicit expressions for the transport coefficients in the linearized equations are given for very low temperatures and for moderately low temperatures below the $\ensuremath{\lambda}$ point.

C. J. Pethick, H. Smith

Franz Mohling, Indira Ramarao, Dion W. J. Shea

In a previous paper, the master-graph formulation of the quantum-statistical theory of quantum fluids was developed. If this formulation is used to calculate the equilibrium properties of quantum fluids, apparent divergences are encountered in the low-temperature limit. In the present paper, we transform this theory by means of a $\ensuremath{\Lambda}$ transformation to overcome these apparent low-temperature divergences. In this transformation, the terms in the theory which gave rise to the apparent low-temperature divergences and which represent the dominant low-temperature contributions are summed explicitly to obtain well-behaved expressions. In addition, a consistent method is developed to obtain the corrections to the dominant low-temperature contributions. Explicit expressions for the $\ensuremath{\Lambda}$-transformed theory are given for the cases of a Bose fluid above the Bose-Einstein condensation temperature and for a Fermi fluid. Finally, the physical implications of the $\ensuremath{\Lambda}$ transformation are discussed.

Vitaly V. Kocharovsky, Vl. V. Kocharovsky