Correlated density matrix theory of boson superfluids
- Institut fuer Theoretische Physik, Universitaet zu Koeln, D-50937 Cologne (Germany)
- McDonnell Center for the Space Sciences and Department of Physics, Washington University, St. Louis, Missouri 63130 (United States)
A variational approach to unified microscopic description of normal and superfluid phases of a strongly interacting Bose system is proposed. We begin through the diagrammatic analysis and synthesis of key distribution functions that characterize the spatial structure and the degree of coherence present in the two phases. The approach centers on functional minimization of the free energy corresponding to a suitable trial form for the many-body density matrix {ital W}({bold R},{bold R}`){proportional_to}{Phi}({bold R}){ital Q}({bold R},{bold R}`){Phi}({bold R}{prime}), with the wave function {Phi} and incoherence factor {ital Q} chosen to 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 {ital Q} was taken as a permanent of short-range two-body statistical bonds. A stratagem applied to the non-interacting Bose gas by Ziff, Uhlenbeck, and Kac is invoked to extend this ansatz to encompass both superfluid and normal phases, while introducing a variational parameter {ital B} that signals the presence of off-diagonal long-range order. The formal development proceeds from a generating functional {Lambda}, defined by the logarithm of the normalization integral {integral}{ital d}{bold R}{Phi}{sup 2}({bold R}){ital Q}({bold R},{bold R}). Construction of the Ursell-Mayer diagrammatic expansion of the generator {Lambda} is followed by renormalization of the statistical bond and of the parameter {ital B}. For {ital B}{equivalent_to}0, previous results for the normal phase are reproduced, whereas for {ital B}{approx_gt}0, corresponding to the superfluid regime, a new class of anomalous contributions appears. Renormalized expansions for the pair distribution function {ital g}({ital r}) and the cyclic distribution function {ital G}{sub {ital cc}}({ital r}) are extracted from {Lambda} by functional differentiation.
- OSTI ID:
- 282799
- Journal Information:
- Annals of Physics (New York), Vol. 243, Issue 2; Other Information: PBD: Nov 1995
- Country of Publication:
- United States
- Language:
- English
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