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Physica A Statistical Mechanics and its Applications

Bose-Einstein condensation and thermodynamic functions of 4He film

W. N. Mei, Y. C. Lee

Published May 1, 1979• 2 citations
Publisher
DOI
10.1016/0378-4371(79)90004-9

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Physical Review Letters•Apr 1, 2004•6 citations
The distinction is made between a condensation temperature in the thermodynamic sense, where the thermodynamic functions have a discontinuity, and an abrupt accumulation (in the statistical mechanical sense) of particles in the ground state of a system. The criterion for the latter is that an integral will not approximate one term of a sum. The problem of a thin film of gas is solved to illustrate this distinction. For films thicker than a critical thickness a condensation occurs at the same temperature as that for bulk material. The thinner films are effectively two dimensional and have an abrupt accumulation temperature lower than the bulk condensation temperature. Films of liquid helium are briefly considered.
Dynamics of Bose-Einstein Condensate (BEC) is treated on the basis of the Mori theory of non-equilibrium thermodynamics in the hydrodynamic region. The local values of conserved quantities, i.e., particle number, momentum and energy, and Ψ(x), the wave function of BEC, are adopted as a complete set of macrovariables. The set of equations of motion thus obtained is useful to describe the dynamical behavior of superfluid 4He near the λ-point. The density of condensate is not conserved, but its equation of motion has the term which is relevant to the renormalization of condensate to superfluid. The expression for the relaxation time τc of condensate density to its local-equilibrium is given and it is shown that the anomaly of τc near the λ-point coincides with the behavior experimentally determined if nc(∂µc/∂nc) is proportional to (Tλ-T) as in the Landau theory of phase transition. In case ωτc ≪1 the ordinary two-fluid hydrodynamics is derived by eliminating the motion of condensate density.
It is shown that the assumption that the many particle wave functions describing superfluid 4He have some phase coherence properties of correlated basis functions provides a new explanation of the link between Bose-Einstein condensation and two fluid behavior. This assumption also implies that the condensate fraction is proportional to the superfluid fraction, in agreement with experiment, and provides a simple quantitative explanation of the anomalous reduction in spatial order and liquid density, observed as the temperature is lowered in superfluid 4He.