ISSN:
1089-7690

Source:
AIP Digital Archive

Topics:
Physics
,
Chemistry and Pharmacology

Notes:
We report the details of a theory which predicts the freezing of quantum liquids, such as helium [J. Chem. Phys. 90, 4622 (1989)]. The freezing of a wide variety of classical liquids has been described by the density functional (DF) theory of statistical mechanics. By choosing a new ideal system, we construct a new DF theory which addresses directly many of the unusual features of the freezing of liquid helium, such as the weakly modulated liquid pair correlation function g(r) at freezing densities. The theory combines DF techniques with the Feynman path integral formulation of quantum mechanics, to include correctly dispersion effects. In classical DF theories, the density and external field of the ideal system are connected by a Boltzmann relation ρ(r)∝exp[−βV(r)]. In our quantum DF theory, we relate the density and external field of the ideal system through the Feynman path integral representation, in which the quantum particle is represented by a classical "ring polymer'' of P beads. In practical applications, the DF perturbation expansion is truncated at second order, and classical DF theories fail for helium because they employ an ideal system which is too far removed from the interacting system. For a certain simplified problem, the density path integral of the ideal system can be performed in closed form, leading to a compact, physically descriptive theory. In a companion paper, the full theory is applied to the freezing of helium-4 and yields good results.

Type of Medium:
Electronic Resource

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