State-of-the-art models for the phase diagram of carbon and diamond nucleation

We review recent developments in the modelling of the phase diagram and the kinetics of crystallization of carbon. In particular, we show that a particular class of bond-order potentials (the so-called LCBOP models) account well for many of the knownstructural and thermodynamic properties of carbon at high pressures and temperatures. We discuss the LCBOP models in some detail. In addition, we briefly review the ``history of experimental and theoretical studies of the phase behaviour of carbon. Using a well-tested version of the LCBOP model (viz. LCBOPI+) we address some of the more controversial hypotheses concerning the phase behaviour of carbon, in particular: the suggestion that liquid carbon can exist in two phases separated by a first-order phase transition and the conjecture that diamonds could have formed by homogeneous nucleation in Uranus and Neptune.

The design of Kinetic Functionals for Many-Body Electron Systems : Combining analytical theory with Monte Carlo sampling of electronic configurations

In a previous work [L.Delle Site, J.Phys.A 40, 2787 (2007)] the derivation of an analytic expression for the kinetic functional of a many-body electron system has been proposed. Though analytical, the formula is still non local (multidimensional) andthus not ideal for numerical applications. In this work, by treating the test case of a uniform gas of interacting spinless electrons, we propose a computational protocol which combines the previous analytic results with the Monte Carlo (MC) sampling of electronic configurations in space. This, we show, leads to an internally consistent scheme to design well founded local kinetic functionals.