BoseEinstein Condensation and Liquid Helium
Abstract
The mathematical description of B.E. (BoseEinstein) condensation is generalized so as to be applicable to a system of interacting particles. B.E. condensation is said to be present whenever the largest eigenvalue of the oneparticle reduced density matrix is an extensive rather than an intensive quantity. Some transformations facilitating the practical use of this definition are given. An argument based on first principles is given, indicating that liquid belium II in equilibrium shows B.E. condensation. For absolute zero, the argument is based on properties of the groundstate wave function derived from the assumption that there is no "longrange configurational order." A crude estimate indicates that roughly 8% of the atoms are "condensed" (note that the fraction of condensed particles need not be identified with ρ_{s}ρ). Conversely, it is shown why one would not expect B.E. condensation in a solid. For finite temperatures Feynman's theory of the lambdatransition is applied: Feynman's approximations are shown to imply that our criterion of B.E. condensation is satisfied below the lambdatransition but not above it.
 Publication:

Physical Review
 Pub Date:
 November 1956
 DOI:
 10.1103/PhysRev.104.576
 Bibcode:
 1956PhRv..104..576P