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Physics Letters A

The strongly-interacting spinless boson fluid: Statistical thermodynamics of the fluid surface

Clive A. Croxton

Published Oct 1, 1972• 1 citation
Publisher
DOI
10.1016/0375-9601(72)90383-0

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A relation between the thermodynamic potential and certain spectral-weight functions in mixed singlet-triplet states of a Fermi fluid with weakly attractive interaction is established. The entire thermodynamics of the system can be derived using this relation. A similar relation is also established for an assembly of spinless, interacting bosons in the ordered phase. The latter corresponds to the Kadanoff-Baym relation for the normal phase when the necessary conditions are fulfilled. Crossover scaling forms for the susceptibility and the deviation of pressure from its critical value for the Bose system are calculated using the established relation. These forms are in general agreement with those obtained earlier by renormalization-group approaches to the problem.
Correlated Density Matrix (CDM) theory permits formal analyses of microscopic properties of strongly correlated quantum fluids and liquids at nonzero temperatures. Equilibrium properties, thermodynamic potentials, correlation and structure functions can be studied formally as well as numerically within the CDM algorithm. Here we provide the essential building blocks for studying the radial distribution function and the single-particle momentum distribution of the ingredients of the quantum systems. We focus on the statistical properties of correlated fluids and introduce the concept of renormalized bosons and fermions. These entities carry the main statistical features of the correlated systems such as liquid 4 He through their specific dependence on temperature, particle number density, and wavenumber encapsulated in their effective masses. The formalism is developed for systems of bosons and of fermions. Numerical calculations for fluid 4 He in the normal phase demonstrate the power of the renormalization concept. The formalism is further extended to analyze the Bose-Einstein condensed phases and gives a microscopic understanding of Tisza's two-fluid model for the normal and superfluid density components.
The equilibrium and quasi-equilibrium properties of a system of interacting bosons are studied from a microscopic point of view. For equilibrium, the model of Bogolyubov is generalized to finite temperature by using the grand partition function. The thermodynamic properties and the pair-correlation function are calculated. The statistical mechanics for moving systems is then developed and applied to the problem of a rotating fluid. For quasi-equilibrium, general transport equations are derived from first principles, independent of statistics and model. For the Bogolyubov model, the familiar two-fluid hydrodynamics is then derived, leading to the phenomena of first and second sound.