CORRELATED DENSITY-MATRIX THEORY OF BOSON SUPERFLUIDS

A variational approach to unified microscopic description of normal an d superfluid phases of a strongly interacting Bose system is proposed. We begin the formulation of an optimal theory within this approach th rough the diagrammatic analysis and synthesis of key distribution func tions that characterize the spatial structure and the degree of cohere nce present in the two phases. The approach centers on functional mini mization of the free energy corresponding to a suitable trial form for the many-body density matrix W(R, R') proportional to Phi(R) Q(R, R') Phi(R'), with the wave function Phi and incoherence factor Q chosen t o incorporate the essential dynamical and statistical correlations. In earlier work addressing the normal phase, Phi was taken as a Jastrow product of two-body dynamical correlation factors and Phi was taken as a permanent of short-range two-body statistical bonds. A stratagem ap plied to the noninteracting Bose gas by Ziff, Uhlenbeck, and Kac is in voked to extend this ansatz to encompass both superfluid and normal ph ases, while introducing a variational parameter B that signals the pre sence of off-diagonal long-range order. The formal development proceed s from a generating Functional Lambda, defined by the logarithm of the normalization integral integral dR Phi(2)(R) Q(R, R). Construction of the Ursell-Mayer diagrammatic expansion of the generator Lambda is fo llowed by renormalization of the statistical bond and of the parameter B. For B = 0, previous results for the normal phase are reproduced, w hereas For B > 0, corresponding to the superfluid regime, a new class of anomalous contributions appears. Renormalized expansions for the pa ir distribution function g(r) and the cyclic distribution function G(c c)(r) are extracted from Lambda by functional differentiation. Standar d diagrammatic techniques are adapted to obtain the appropriate hypern etted-chain equations for the evaluation of these spatial distribution functions. Corresponding results are presented for the internal energ y. The quantity G(cc)(r) is found to develop long-range order in the c ondensed phase and therefore, assumes an incisive diagnostic role in t he elucidation of the Bose-Einstein transition of the interacting syst em. A tentative connection of the microscopic description with the phe nomenological two-fluid model is established in terms of a sum rule on ''normal'' and ''anomalous'' density components. Further work within this correlated density matrix approach will address the one-body dens ity matrix, the entropy, and the Euler-Lagrange equations that lead to an optimal theory. (C) 1995 Academic Press, Inc.