The Decay Properties of the Finite Temperature Density Matrix in Metals

Using ordinary Fourier analysis, the asymptotic decay behavior of the density matrix F(r,r') is derived for the case of a metal at a finite electronic temperature. An oscillatory behavior which is damped exponentially with increasing distance between r and r' is found. The decay rate is not only determined by the electronic temperature, but also by the Fermi energy. The theoretical predictions are confirmed by numerical simulations

Thermal analysis of submicron nanocrystalline diamond films

The thermal properties of sub-μm nanocrystalline diamond films in the range of 0.37–1.1 μm grown by hot filament CVD, initiated by bias enhanced nucleation on a nm-thin Si-nucleation layer on various substrates, have been characterized by scanning thermal microscopy. After coalescence, the films have been outgrown with a columnar grain structure. The results indicate that even in the sub-μm range, the average thermal conductivity of these NCD films approaches 400 W m− 1 K− 1. By patterning the films into membranes and step-like mesas, the lateral component and the vertical component of the thermal conductivity, k<sub>lateral</sub> and k<sub>vertical</sub>, have been isolated showing an anisotropy between vertical conduction along the columns, with k<sub>vertical</sub> ≈ 1000 W m− 1 K− 1, and a weaker lateral conduction across the columns, with k<sub>lateral</sub> ≈ 300 W m− 1 K− 1

Electron Paramagnetic Resonance of Boron Acceptors in Isotopically Purified Silicon

The electron paramagnetic resonance (EPR) linewidths of B acceptors in Si are found to reduce dramatically in isotopically purified 28Si single crystals. Moreover, extremely narrow substructures in the EPR spectra are visible corresponding to either an enhancement or a reduction of the absorbed microwave on resonance. The origin of the substructures is attributed to a combination of simultaneous double excitation and spin relaxation in the four level spin system of the acceptors. A spin population model is developed which qualitatively describes the experimental results.Comment: 4 pages, 3 figure

Total energy global optimizations using non orthogonal localized orbitals

An energy functional for orbital based $O(N)$ calculations is proposed, which depends on a number of non orthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical potential, determining the number of electrons. We show that the minimization of the functional with respect to overlapping localized orbitals can be performed so as to attain directly the ground state energy, without being trapped at local minima. The present approach overcomes the multiple minima problem present within the original formulation of orbital based $O(N)$ methods; it therefore makes it possible to perform $O(N)$ calculations for an arbitrary system, without including any information about the system bonding properties in the construction of the input wavefunctions. Furthermore, while retaining the same computational cost as the original approach, our formulation allows one to improve the variational estimate of the ground state energy, and the energy conservation during a molecular dynamics run. Several numerical examples for surfaces, bulk systems and clusters are presented and discussed.Comment: 24 pages, RevTex file, 5 figures available upon reques

Evidence for a Far-Traveled Thrust Sheet in the Greater Himalayan Thrust System, and an Alternative Model to Building the Himalaya

The Galchhi shear zone underlies the Kathmandu klippe in central Nepal and has emerged as a key structure for discriminating competing models for the formation of the Himalayan orogenic wedge. New chronologic data from the Galchhi area suggest a new structural and orogenic interpretation. Zircons from quartzites and an orthogneiss restrict protolith deposition to between 467+7/ – 10 Ma and ~570 Ma, with metamorphic zircon growth at 23-29 Ma. Comparable data from the Greater Himalayan Sequence (GHS) at the intra-GHS Langtang thrust, north of Galchhi, similarly restrict GHS deposition to between 475+7/ – 3 and ~660 Ma. Undeformed pegmatites near Galchhi constrain movement of the Galchhi shear zone to ≥22.5 ± 2.3 Ma, long before slip of the Main Central Thrust in the region (≤17 Ma). Shear sense indicators in the Galchhi area indicate both top-to-the-south and top-to-the-north shears. The old age of movement, Neoproterozoic youngest detrital zircons, occurrence of top-to-the-south shear sense indicators, and intrusive Paleozoic granites, all suggest that the Galchhi shear zone is an intra-GHS top-to-the-south thrust, rather than either a thrust involving Lesser Himalayan rocks, or a top-to-the-north shear zone that juxtaposed Tethyan and GHS rocks during coeval movement of the Main Central Thrust. The GHS in Nepal was not emplaced as a single body of rock but consists of at least two ductile “thrust sheets,” present in both the hinterland at Langtang and toward the foreland at Galchhi. GHS thrust sheets sequentially underplated during southward propagation of the thrust belt

Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous isotropic concentric layers is further proposed based on the effective medium theory. This cloak is characterised by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with a inhomogeneous and anisotropic distribution of material parameters. The latter suffers from singular material parameters on its inner surface. This singularity depends upon the sharpness of corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak becomes more and more singular when the number of vertices increases if it is star shaped. We thus analyse the acoustic response of a non-singular spherical cloak designed by blowing up a small ball instead of a point, as proposed in [Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The multilayered approximation of this cloak requires less extreme densities (especially for the lowest bound). Finally, we investigate another type of non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev. Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloak

Linking entanglement and quantum phase transitions via density functional theory

Density functional theory (DFT) is shown to provide a novel conceptual and computational framework for entanglement in interacting many-body quantum systems. DFT can, in particular, shed light on the intriguing relationship between quantum phase transitions and entanglement. We use DFT concepts to express entanglement measures in terms of the first or second derivative of the ground state energy. We illustrate the versatility of the DFT approach via a variety of analytically solvable models. As a further application we discuss entanglement and quantum phase transitions in the case of mean field approximations for realistic models of many-body systems.Comment: 6 pages, 2 figure

Two-Dimensional Sigma-Hole Systems in Boron Layers: A First-Principles Study on Mg_{1-x}Na_xB_2 and Mg_{1-x}Al_xB_2

We study two-dimensional sigma-hole systems in boron layers by calculating the electronic structures of Mg_{1-x}Na_xB_2 and Mg_{1-x}Al_xB_2. In Mg_{1-x}Na_xB_2, it is found that the concentration of sigma holes is approximately described by (0.8 + 0.8 x) * 10^{22} cm^{-3} and the largest attainable concentration is about 1.6 * 10^{22} cm^{-3} in NaB_2. In Mg_{1-x}Al_xB_2, on the other hand, it is found that the concentration of sigma holes is approximately described by (0.8 - 1.4 x) * 10^{22} cm^{-3} and sigma holes are disappeared at x of about 0.6. These relations can be used for experimental studies on the sigma-hole systems in these materials.Comment: 5 pages, 5 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

Itinerant in-plane magnetic fluctuations and many-body correlations in Nax_xCoO2_2

Based on the {\it ab-initio} band structure for Na$_x$CoO$_2$ we derive the single-electron energies and the effective tight-binding description for the $t_{2g}$ bands using projection procedure. Due to the presence of the next-nearest-neighbor hoppings a local minimum in the electronic dispersion close to the $\Gamma$ point of the first Brillouin zone forms. Correspondingly, in addition to a large Fermi surface an electron pocket close to the $\Gamma$ point emerges at high doping concentrations. The latter yields the new scattering channel resulting in a peak structure of the itinerant magnetic susceptibility at small momenta. This indicates dominant itinerant in-plane ferromagnetic fluctuations above certain critical concentration $x_m$, in agreement with neutron scattering data. Below $x_m$ the magnetic susceptibility shows a tendency towards the antiferromagnetic fluctuations. We further analyze the many-body effects on the electronic and magnetic excitations using various approximations applicable for different $U/t$ ratio.Comment: 10 page