Correlated one-body density matrix of boson superfluids

Abstract

The correlated density matrix theory is employed and further developed to analyze the one-body density matrix ρ1(|r1-r2|) of the normal and superfluid phases of a strongly interacting Bose system at non-zero temperature. The approach continues the formal development described in an earlier article and is based on a suitable trial ansatz for the many-body density matrixW(R, R′)∼Φ(R) Q(R, R′) Φ(R′) with the wave function Φ and incoherence factorQ incorporating the essential statistical and dynamical correlations. Special attention is given to the appearance of off-diagonal long-range order in function ρ1(|r1-r2|) and its relation to the condensation strength Bcc characterizing the degree of coherence in the superfluid phase. We derive a number of structural relations that have counterparts in known results on ρ1 in the Jastrow variational theory of the Bose ground state. We discuss Bose-Einstein condensation and make contact to Landau's phenomenological theory of continuous phase transitions. Numerical estimates are presented on the condensation strength and the condensate fraction of liquid4He as functions of the temperature.