Bose-Einstein Condensation and the (lambda)Transition in Liquid Helium

Integrating seminal ideas of London, Feynman, Uhlenbeck, Bloch, Bardeen, and other illustrious antecessors, this paper continues the development of an ab initio theory of the (lambda)transition in liquid 4He. The theory is based upon variational determination of a correlated density matrix suitable for description of both normal and superfluid phases, within an approach that extends to finite temperatures the very successful correlated wave-functions theory of the ground state and elementary excitations at zero temperature. We present the results of a full optimization of a correlated trial form for the density matrix that includes the effects both of temperature-dependent dynamical correlations and of statistical correlations corresponding to thermal phonon/roton and quasiparticle/hole excitations-all at the level of two-point descriptors. The optimization process involves constrained functional minimization of the associated free energy through solution of a set of Euler-Lagrange equations, consisting of a generalized paired-phonon equation for the structure function, an analogous equation for the Fourier transform of the statistical exchange function, and a Feynman equation for the dispersion law of the collective excitations. Violation of particle-hole exchange symmetry emerges as an important aspect of the transition, along with broken gauge symmetry. In conjunction with a semi-phenomenological study in which renormalized masses are introduced for quasiparticle/hole and collective excitations, the results suggest that a quantitative description of the (lambda)transition and associated thermodynamic quantities can be achieved once the trial density matrix is modified-notably through the addition of three-point descriptors-to include backflow effects and allow for ab initio treatment of important variations in effective masses.