Relevance of coordinate and particle-number scaling in density functional theory

We discuss a $\beta$-dependent family of electronic density scalings of the form $n_\lambda(\R)=\lambda^{3\beta+1}\; n(\lambda^\beta \R)$ in the context of density functional theory. In particular, we consider the following special cases: the Thomas-Fermi scaling ($\beta=1/3$ and $\lambda \gg 1$), which is crucial for the semiclassical theory of neutral atoms; the uniform-electron-gas scaling ($\beta=-1/3$ and $\lambda\gg 1$), that is important in the semiclassical theory of metallic clusters; the homogeneous density scaling ($\beta=0$) which can be related to the self-interaction problem in density functional theory when $\lambda \leq 1$; the fractional scaling ($\beta=1$ and $\lambda\leq 1$), that is important for atom and molecule fragmentation; and the strong-correlation scaling ($\beta=-1$ and $\lambda \gg 1$) that is important to describe the strong correlation limit. The results of our work provide evidence for the importance of this family of scalings in semiclassical and quantum theory of electronic systems, and indicate that these scaling properties must be considered as important constraints in the construction of new approximate density functionals. We also show, using the uniform-electron-gas scaling, that the curvature energy of metallic clusters is related to the second-order gradient expansion of kinetic and exchange-correlation energies.Comment: 13 pages, 3 figures, accepted for publication on PR

Two distinct desynchronization processes caused by lesions in globally coupled neurons

To accomplish a task, the brain works like a synchronized neuronal network where all the involved neurons work together. When a lesion spreads in the brain, depending on its evolution, it can reach a significant portion of relevant area. As a consequence, a phase transition might occur: the neurons desynchronize and cannot perform a certain task anymore. Lesions are responsible for either disrupting the neuronal connections or, in some cases, for killing the neuron. In this work, we will use a simplified model of neuronal network to show that these two types of lesions cause different types of desynchronization.Comment: 5 pages, 3 figure

Kinetic and Exchange Energy Densities near the Nucleus

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.Comment: 11 pages, 7 figure

Negative-U properties for substitutional Au in Si

The isolated substitutional gold impurity in bulk silicon is studied in detail using electronic structure calculations based on density-functional theory. The defect system is found to be a non-spin-polarized negative-U centre, thus providing a simple solution to the long-standing debate over the electron paramagnetic resonance signal for gold in silicon. There is an excellent agreement (within 0.03 eV) between the well-established experimental donor and acceptor levels and the predicted stable charge state transition levels, allowing for the unambiguous assignment of the two experimental levels to the (1+/1-) and (1-/3-) transitions, respectively, in contrast to previously held assumptions about the system.Comment: 6 pages, 5 figure