Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory

URL:http://link.aps.org/doi/10.1103/PhysRevLett.77.2037 DOI:10.1103/PhysRevLett.77.2037The frequency-dependent exchange-correlation potential, which appears in the usual Kohn- Sham formulation of a time-dependent linear response problem, is a strongly nonlocal functional of the density, so that a consistent local density approximation generally does not exist. This problem can be avoided by choosing the current density as the basic variable in a generalized Kohn-Sham theory. This theory admits a local approximation which, for fixed frequency, is exact in the limit of slowly varying densities and perturbing potentials.We acknowledge support from NSF Grants No. DMR- 9403908 and No. DMR-9308011

Edge Electron Gas

The uniform electron gas, the traditional starting point for density-based many-body theories of inhomogeneous systems, is inappropriate near electronic edges. In its place we put forward the appropriate concept of the edge electron gas.Comment: 4 pages RevTex with 7 ps-figures included. Minor changes in title,text and figure

Stable isotope evidence for crustal recycling as recorded by superdeep diamonds

© 2015 Elsevier B.V. Sub-lithospheric diamonds from the Juina-5 and Collier-4 kimberlites and the Machado River alluvial deposit in Brazil have carbon isotopic compositions that co-vary with the oxygen isotopic compositions of their inclusions, which implies that they formed by a mixing process. The proposed model for this mixing process, based on interaction of slab-derived carbonate melt with reduced (carbide- or metal-bearing) ambient mantle, explains these isotopic observations. It is also consistent with the observed trace element chemistries of diamond inclusions from these localities and with the experimental phase relations of carbonated subducted crust. The 18O-enriched nature of the inclusions demonstrates that they incorporate material from crustal protoliths that previously interacted with seawater, thus confirming the subduction-related origin of superdeep diamonds. These samples also provide direct evidence of an isotopically anomalous reservoir in the deep (≥350 km) mantle

Band structure analysis of the conduction-band mass anisotropy in 6H and 4H SiC

The band structures of 6H and 4H SiC calculated by means of the FP-LMTO method are used to determine the effective mass tensors for their conduction-band minima. The results are shown to be consistent with recent optically detected cyclotron resonance measurements and predict an unusual band filling dependence for 6H-SiC.Comment: 5 pages including 4 postscript figures incorporated with epsfig figs. available as part 2: sicfig.uu self-extracting file to appear in Phys. Rev. B: Aug. 15 (Rapid Communications

Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies

The statistical mechanics of periodically driven ("Floquet") systems in contact with a heat bath exhibits some radical differences from the traditional statistical mechanics of undriven systems. In Floquet systems all quasienergies can be placed in a finite frequency interval, and the number of near degeneracies in this interval grows without limit as the dimension N of the Hilbert space increases. This leads to pathologies, including drastic changes in the Floquet states, as N increases. In earlier work these difficulties were put aside by fixing N, while taking the coupling to the bath to be smaller than any quasienergy difference. This led to a simple explicit theory for the reduced density matrix, but with some major differences from the usual time independent statistical mechanics. We show that, for weak but finite coupling between system and heat bath, the accuracy of a calculation within the truncated Hilbert space spanned by the N lowest energy eigenstates of the undriven system is limited, as N increases indefinitely, only by the usual neglect of bath memory effects within the Born and Markov approximations. As we seek higher accuracy by increasing N, we inevitably encounter quasienergy differences smaller than the system-bath coupling. We therefore derive the steady state reduced density matrix without restriction on the size of quasienergy splittings. In general, it is no longer diagonal in the Floquet states. We analyze, in particular, the behavior near a weakly avoided crossing, where quasienergy near degeneracies routinely appear. The explicit form of our results for the denisty matrix gives a consistent prescription for the statistical mechanics for many periodically driven systems with N infinite, in spite of the Floquet state pathologies.Comment: 31 pages, 3 figure

Time Dependent Floquet Theory and Absence of an Adiabatic Limit

Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as N goes to infinity, the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high order resonances). This paper deals with the highly non-trivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude, lambda. The mathematical radii of convergence of perturbation theory in lambda approach zero. There is no adiabatic limit of the wave functions when lambda is turned on arbitrarily slowly. However, the quasienergy becomes independent of time in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit N goes to infinity, the conventional approaches are appropriate in almost all physically interesting situations.Comment: 13 pages, Latex, plus 2 Postscript figure

Stable isotope evidence for crustal recycling as recorded by superdeep diamonds

Sub-lithospheric diamonds from the Juina-5 and Collier-4 kimberlites and the Machado River alluvial deposit in Brazil have carbon isotopic compositions that co-vary with the oxygen isotopic compositions of their inclusions, which implies that they formed by a mixing process. The proposed model for this mixing process, based on interaction of slab-derived carbonate melt with reduced (carbide- or metal-bearing) ambient mantle, explains these isotopic observations. It is also consistent with the observed trace element chemistries of diamond inclusions from these localities and with the experimental phase relations of carbonated subducted crust. The 18O-enriched nature of the inclusions demonstrates that they incorporate material from crustal protoliths that previously interacted with seawater, thus confirming the subduction-related origin of superdeep diamonds. These samples also provide direct evidence of an isotopically anomalous reservoir in the deep (≥350 km) mantle

Structure of liquid tricalcium aluminate

International audienceThe atomic-scale structure of aerodynamically levitated and laser-heated liquid tricalcium aluminate (Ca 3 Al 2 O 6) was measured at 2073(30) K by using the method of neutron diffraction with Ca isotope substitution (NDIS). The results enable the detailed resolution of the local coordination environment around calcium and aluminum atoms, including the direct determination of the liquid partial structure factor, S CaCa (Q), and partial pair distribution function, g CaCa (r). Molecular dynamics (MD) simulation and reverse Monte Carlo (RMC) refinement methods were employed to obtain a detailed atomistic model of the liquid structure. The composition Ca 3 Al 2 O 6 lies at the CaO-rich limit of the CaO:Al 2 O 3 glass-forming system. Our results show that, although significantly depolymerized, liquid Ca 3 Al 2 O 6 is largely composed of AlO 4 tetrahedra forming an infinite network with a slightly higher fraction of bridging oxygen atoms than expected for the composition. Calcium-centered polyhedra exhibit a wide distribution of four-to sevenfold coordinated sites, with higher coordinated calcium preferentially bonding to bridging oxygens. Analysis of the MD configuration reveals the presence of ∼10 % unconnected AlO 4 monomers and Al 2 O 7 dimers in the liquid. As the CaO concentration increases, the number of these isolated units increases, such that the upper value for the glass-forming composition of CaO:Al 2 O 3 liquids could be described in terms of a percolation threshold at which the glass can no longer support the formation of an infinitely connected AlO 4 network