The Exact Ground State of a Boson Hard Sphere Fluid

Mark Dewing, David M. Ceperley

P. Bocchieri, C. A. Orzalesi

P. Bocchieri, C. A. Orzalesi, V. H. Smith

M. A. Solís, MANUEL DE LLANO, J. W. Clark +1 more

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a "sphere-of-influence" picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate regular (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are constructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, extrapolated to intermediate densities via Padé and other approximants, but whose ultimate density is irregular or random closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L -expansion data for two-component fermions.

Douglas J. Henderson

In the tunnel model, a fluid is regarded as being composed of rows of molecules, which move almost in one dimension along lines or tunnels, the walls of which are formed by neighboring rows of molecules. This model provides a simple and reliable theory for a classical system of dense hard spheres. The tunnel model has also been applied to quantum hard spheres. However, until recently, there have been no reliable results for dense quantum hard spheres, so that the accuracy of the quantum tunnel model could not be judged. Comparison with a recent variational determination of the ground-state energy of a system of hard spheres shows that the tunnel model is reliable for this system.

Aycan Yurtsever, B. Tanatar