Entanglement degree measure and a criterion for sudden death as a phase transition in bipartite systems

We propose a method to compute the entanglement degree E of bipartite systems having dimension 2 x 2 and demonstrate that the partial transposition of density matrix, the Peres criterion, arise as a consequence Of Our method. Differently from other existing measures of entanglement, the one presented here makes possible the derivation of a criterion to verify if an arbitrary bipartite entanglement will suffers sudden death (SD) based only on the initial-state parameters. Our method also makes possible to characterize the SD as a dynamical quantum phase transition, with order parameter epsilon. having a universal critical exponent -1/2. (C) 2009 Elsevier Inc. All rights reserved.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Orbital-polarization terms: From a phenomenological to a first-principles description of orbital magnetism in density-functional theory

Phenomenological orbital-polarizition (OP) terms have been repeatedly introduced in the single-particle equations of spin-density-functional theory, in order to improve the description of orbital magnetic moments in systems containing transition metal ions. Here we show that these ad hoc corrections can be interpreted as approximations to the exchange-correlation vector potential A(xc) of current-density functional theory (CDFT). This connection provides additional information on both approaches: phenomenological OP terms are connected to first-principles theory, leading to a rationale for their empirical success and a reassessment of their limitations and the approximations made in their derivation. Conversely, the connection of OP terms with CDFT leads to a set of simple approximations to the CDFT potential A(xc), with a number of desirable features that are absent from electron-gas-based functionals. (C) 2008 Wiley Periodicals, Inc.

Microgranitic Enclaves as Products of Self-mixing Events: a Study of Open-system Processes in the Maua Granite, Sao Paulo, Brazil, Based on in situ Isotopic and Trace Elements in Plagioclase

Felsic microgranular enclaves with structures indicating that they interacted in a plastic state with their chemically similar host granite are abundant in the Maua Pluton, SE Brazil. Larger plagioclase xenocrysts are in textural disequilibrium with the enclave groundmass and show complex zoning patterns with partially resorbed An-rich cores (locally with patchy textures) surrounded by more sodic rims. In situ laser ablation-(multi-collector) inductively coupled plasma mass spectrometry trace element and Sr isotopic analyses performed on the plagioclase xenocrysts indicate open-system crystallization; however, no evidence of derivation from more primitive basic melts is observed. The An-rich cores have more radiogenic initial Sr isotopic ratios that decrease towards the outermost part of the rims, which are in isotopic equilibrium with the matrix plagioclase. These profiles may have been produced by either (1) diffusional re-equilibration after rim crystallization from the enclave-forming magma, as indicated by relatively short calculated residence times, or (2) episodic contamination with a decrease of the contaminant ratio proportional to the extent to which the country rocks were isolated by the crystallization front. Profiles of trace elements with high diffusion coefficients would require unrealistically long residence times, and can be modeled in terms of fractional crystallization. A combination of trace element and Sr isotope data suggests that the felsic microgranular enclaves from the Maua Pluton are the products of interaction between end-member magmas that had similar compositions, thus recording `self-mixing` events.

Alkaline magmatism in the Amambay area, NE Paraguay: The Cerro Sarambi complex

The Early Cretaceous alkaline magmatism in the northeastern region of Paraguay (Amambay Province) is represented by stocks, plugs, dikes, and dike swarms emplaced into Carboniferous to Triassic-Jurassic sediments and Precambrian rocks. This magmatism is tectonically related to the Ponta Pora Arch, a NE-trending structural feature, and has the Cerro Sarambi and Cerro Chiriguelo carbonatite complexes as its most significant expressions. Other alkaline occurrences found in the area are the Cerro Guazu and the small bodies of Cerro Apua, Arroyo Gasory, Cerro Jhu, Cerro Tayay, and Cerro Teyu. The alkaline rocks comprise ultramafic-mafic, syenitic, and carbonatitic petrographic associations in addition to lithologies of variable composition and texture occurring as dikes; fenites are described in both carbonatite complexes. Alkali feldspar and clinopyroxene, ranging from diopside to aegirine, are the most abundant minerals, with feldspathoids (nepheline, analcime), biotite, and subordinate Ti-rich garnet; minor constituents are Fe-Ti oxides and cancrinite as the main alteration product from nepheline. Chemically, the Amambay silicate rocks are potassic to highly potassic and have miaskitic affinity, with the non-cumulate intrusive types concentrated mainly in the saturated to undersaturated areas in silica syenitic fields. Fine-grained rocks are also of syenitic affiliation or represent more mafic varieties. The carbonatitic rocks consist dominantly of calciocarbonatites. Variation diagrams plotting major and trace elements vs. SiO(2) concentration for the Cerro Sarambi rocks show positive correlations for Al(2)O(3), K(2)O, and Rb, and negative ones for TiO(2), MgO, Fe(2)O(3), CaO, P(2)O(5), and Sr, indicating that fractional crystallization played an important role in the formation of the complex. Incompatible elements normalized to primitive mantle display positive spikes for Rb, La, Pb, Sr, and Sm, and negative for Nb-Ta, P, and Ti, as these negative anomalies are considerably more pronounced in the carbonatites. Chondrite-normalized REE patterns point to the high concentration of these elements and to the strong LRE/HRE fractionation. The Amambay rocks are highly enriched in radiogenic Sr and have T(DM) model ages that vary from 1.6 to 1.1 Ga. suggesting a mantle source enriched in incompatible elements by metasomatic events in Paleo-Mesoproterozoic times. Data are consistent with the derivation of the Cerro Sarambi rocks from a parental magma of lamprophyric (minette) composition and suggest an origin by liquid immiscibility processes for the carbonatites. (C) 2011 Elsevier Ltd. All rights reserved.