16 research outputs found
Induced Charge-Density Oscillations at Metal Surfaces
Induced charge-density (ICD) oscillations at the Cu(111) surface caused by an
external impurity are studied within linear response theory. The calculation
takes into account such properties of the Cu(111) surface electronic structure
as an energy gap for three-dimensional (3D) bulk electrons and a
surface state that forms two-dimensional (2D) electron system. It is
demonstrated that the coexistence of these 2D and 3D electron systems has
profound impact on the ICD in the surface region. In the case of a static
impurity the characteristic ICD oscillations with the decay as a
function of lateral distance, , are established in both electron systems.
For the impurity with a periodically time-varying potential, the novel dominant
ICD oscillations which fall off like are predicted.Comment: 11 pages, 5 figure
Diagrammatic self-energy approximations and the total particle number
There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin's G(0)W(0) approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated
Topology and correlations in structured scale-free networks
We study a recently introduced class of scale-free networks showing a high
clustering coefficient and non-trivial connectivity correlations. We find that
the connectivity probability distribution strongly depends on the fine details
of the model. We solve exactly the case of low average connectivity, providing
also exact expressions for the clustering and degree correlation functions. The
model also exhibits a lack of small world properties in the whole parameters
range. We discuss the physical properties of these networks in the light of the
present detailed analysis.Comment: 10 pages, 9 figure
Mesoscopics and fluctuations in networks
We describe fluctuations in finite-size networks with a complex distribution
of connections, . We show that the spectrum of fluctuations of the number
of vertices with a given degree is Poissonian. These mesoscopic fluctuations
are strong in the large-degree region, where ( is the
total number of vertices in a network), and are important in networks with
fat-tailed degree distributions.Comment: 3 pages, 1 figur
Does Complex Learning Require Complex Connectivity?
Small World and Scale Free network properties characterize many real complex phenomena. We assume that low level connectivity with such topological properties, e.g., anatomical or functional connectivity in brains, is compulsory to achieve high level cognitive functionality, as language. The study of these network properties provides tools to approach different issues in behavior based Artificial Intelligence (AI) that usually have been ill defined, e.g., complexity and autonomy. In this paper, we propose a model in which situated agents evolve knowledge networks holding both Small World and Scale Free properties. Experimental results in the context of Pragmatic Games, elucidate some required conditions to obtain the expected network properties when performing complex learning