Alloying effects on the optical properties of Ge1−x_{1-x}Six_x nanocrystals from TDDFT and comparison with effective-medium theory

We present the optical spectra of Ge$_{1-x}$Si$_x$ alloy nanocrystals calculated with time-dependent density-functional theory in the adiabatic local-density ap proximation (TDLDA). The spectra change smoothly as a function of the compositio n $x$. On the Ge side of the composition range, the lowest excitations at the ab sorption edge are almost pure Kohn-Sham independent-particle HOMO-LUMO transitio ns, while for higher Si contents strong mixing of transitions is found. Within T DLDA the first peak is slightly higher in energy than in earlier independent-par ticle calculations. However, the absorption onset and in particular its composit ion dependence is similar to independent-particle results. Moreover, classical depolarization effects are responsible for a very strong suppression of the abs orption intensity. We show that they can be taken into account in a simpler way using Maxwell-Garnett classical effective-medium theory. Emission spectra are in vestigated by calculating the absorption of excited nanocrystals at their relaxe d geometry. The structural contribution to the Stokes shift is about 0.5 eV. Th e decomposition of the emission spectra in terms of independent-particle transit ions is similar to what is found for absorption. For the emission, very weak tra nsitions are found in Ge-rich clusters well below the strong absorption onset.Comment: submitted to Phys. Rev.

Focusing of opinions in the Deffuant model: First impression counts

The paper treats opinion dynamics of an unequal distribution as the initial opinion distribution. Simulated is the Deffuant model on a directed Barabasi-Albert network with discrete opinions and several subjects. Noticed is a focusing of the the resulting opinion distribution during the simulation towards the average value of the initial opinion distribution. A small change of the focusing is seen. A dependency of this change on the number of subjects and opinions is detected and indicates the change as a consequence of discretization the opinions. Hereby the average value of the initial opinion distribution can be identified as the guide of opinion forming.Comment: 8 pages including 5 figures, for Int. J. Mod. Phys.

Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

Modeling the Local Warm/Hot Bubble

In this paper we review the modeling of the Local Bubble (LB) with special emphasis on the progress we have made since the last major conference "The Local Bubble and Beyond (I)" held in Garching in 1997. Since then new insight was gained into the possible origin of the LB, with a moving group crossing its volume during the last 10 - 15 Myr being most likely responsible for creating a local cavity filled with hot recombining gas. Numerical high resolution 3D simulations of a supernova driven inhomogeneous interstellar medium show that we can reproduce both the extension of the LB and the OVI column density in absorption measured with FUSE for a LB age of 13.5 - 14.5 Myr. We further demonstrate that the LB evolves like an ordinary superbubble expanding into a density stratified medium by comparing analytical 2D Kompaneets solutions to NaI contours, representing the extension of the local cavity. These results suggest that LB blow-out into the Milky Way halo has occurred roughly 5 Myr ago.Comment: 8 pages, 3 figures, to appear in the proceedings of "The Local Bubble and Beyond II", Philadelphia, USA, April 21-24, 200

A time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities

We present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, we implemented it in a real-space (basis-set free) code, and applied it to benchmark molecules, namely CO, H2O, and paranitroaniline (PNA). Our results are in agreement with experimental and previous theoretical studies, and fully validate our approach.Comment: 9 pages, 4 figure

L1599B: Cloud Envelope and C+ Emission in a Region of Moderately Enhanced Radiation Field

We study the effects of an asymmetric radiation field on the properties of a molecular cloud envelope. We employ observations of carbon monoxide (12CO and 13CO), atomic carbon, ionized carbon, and atomic hydrogen to analyze the chemical and physical properties of the core and envelope of L1599B, a molecular cloud forming a portion of the ring at approximately 27 pc from the star Lambda Ori. The O III star provides an asymmetric radiation field that produces a moderate enhancement of the external radiation field. Observations of the [CII] fine structure line with the GREAT instrument on SOFIA indicate a significant enhanced emission on the side of the cloud facing the star, while the [Ci], 12CO and 13CO J = 1-0 and 2-1, and 12CO J = 3-2 data from the PMO and APEX telescopes suggest a relatively typical cloud interior. The atomic, ionic, and molecular line centroid velocities track each other very closely, and indicate that the cloud may be undergoing differential radial motion. The HI data from the Arecibo GALFA survey and the SOFIA/GREAT [CII] data do not suggest any systematic motion of the halo gas, relative to the dense central portion of the cloud traced by 12CO and 13CO.Comment: 9 Figure

On the relation between virial coefficients and the close-packing of hard disks and hard spheres

The question of whether the known virial coefficients are enough to determine the packing fraction $\eta_\infty$ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pad\'e approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that $\eta_\infty$ is equal to the maximum packing fraction corresponding to an ordered crystalline structure.Comment: 10 pages, 6 figures; v2: discussion about hard-square and hard-hexagon systems on a lattice added; five new reference

Critical behavior of a Ginzburg-Landau model with additive quenched noise

We address a mean-field zero-temperature Ginzburg-Landau, or \phi^4, model subjected to quenched additive noise, which has been used recently as a framework for analyzing collective effects induced by diversity. We first make use of a self-consistent theory to calculate the phase diagram of the system, predicting the onset of an order-disorder critical transition at a critical value {\sigma}c of the quenched noise intensity \sigma, with critical exponents that follow Landau theory of thermal phase transitions. We subsequently perform a numerical integration of the system's dynamical variables in order to compare the analytical results (valid in the thermodynamic limit and associated to the ground state of the global Lyapunov potential) with the stationary state of the (finite size) system. In the region of the parameter space where metastability is absent (and therefore the stationary state coincide with the ground state of the Lyapunov potential), a finite-size scaling analysis of the order parameter fluctuations suggests that the magnetic susceptibility diverges quadratically in the vicinity of the transition, what constitutes a violation of the fluctuation-dissipation relation. We derive an effective Hamiltonian and accordingly argue that its functional form does not allow to straightforwardly relate the order parameter fluctuations to the linear response of the system, at odds with equilibrium theory. In the region of the parameter space where the system is susceptible to have a large number of metastable states (and therefore the stationary state does not necessarily correspond to the ground state of the global Lyapunov potential), we numerically find a phase diagram that strongly depends on the initial conditions of the dynamical variables.Comment: 8 figure

On the calculation of the bandgap of periodic solids with MGGA functionals using the total energy

During the last few years, it has become more and more clear that functionals of the meta generalized gradient approximation (MGGA) are more accurate than GGA functionals for the geometry and energetics of electronic systems. However, MGGA functionals are also potentially more interesting for the electronic structure, in particular, when the potential is nonmultiplicative (i.e., when MGGAs are implemented in the generalized Kohn-Sham framework), which may help to get more accurate bandgaps. Here, we show that the calculation of bandgap of solids with MGGA functionals can also be done very accurately in a non-self-consistent manner. This scheme uses only the total energy and can, therefore, be very useful when the self-consistent implementation of a particular MGGA functional is not available. Since self-consistent MGGA calculations may be difficult to converge, the non-self-consistent scheme may also help to speed up the calculations. Furthermore, it can be applied to any other types of functionals, for which the implementation of the corresponding potential is not trivial