Quantum Monte Carlo Impurity Solver for Cluster DMFT and Electronic Structure Calculations in Adjustable Base

We generalized the recently introduced new impurity solver based on the diagrammatic expansion around the atomic limit and Quantum Monte Carlo summation of the diagrams. We present generalization to the cluster of impurities, which is at the heart of the cluster Dynamical Mean-Field methods, and to realistic multiplet structure of a correlated atom, which will allow a high precision study of actinide and lanthanide based compounds with the combination of the Dynamical Mean-Field theory and band structure methods. The approach is applied to both, the two dimensional Hubbard and t-J model within Cellular Dynamical Mean Field method. The efficient implementation of the new algorithm, which we describe in detail, allows us to study coherence of the system at low temperature from the underdoped to overdoped regime. We show that the point of maximal superconducting transition temperature coincides with the point of maximum scattering rate although this optimal doped point appears at different electron densities in the two models. The power of the method is further demonstrated on the example of the Kondo volume collapse transition in Cerium. The valence histogram of the DMFT solution is presented showing the importance of the multiplet splitting of the atomic states.Comment: 12 pages, 4 figure

X-ray absorption spectra at the Ca-L2,3_{2,3}-edge calculated within multi-channel multiple scattering theory

We report a new theoretical method for X-ray absorption spectroscopy (XAS) in condensed matter which is based on the multi-channel multiple scattering theory of Natoli et al. and the eigen-channel R-matrix method. While the highly flexible real-space multiple scattering (RSMS) method guarantees a precise description of the single-electron part of the problem, multiplet-like electron correlation effects between the photo-electron and localized electrons can be taken account for in a configuration interaction scheme. For the case where correlation effects are limited to the absorber atom, a technique for the solution of the equations is devised, which requires only little more computation time than the normal RSMS method for XAS. The new method is described and an application to XAS at the Ca $L_{2,3}$-edge in bulk Ca, CaO and CaF$_2$ is presented.Comment: 10 pages, 4 figures, submitted to Phys. Rev.

Path integral evaluation of equilibrium isotope effects

A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of 60 at 500 K. We describe the implementation of the methodology in the molecular dynamics package Amber 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio potentials to evaluate the equilibrium isotope effects within the harmonic approximation, and then the path integral method together with semiempirical potentials to evaluate the anharmonicity corrections. Our calculations show that the anharmonicity effects amount up to 30% of the symmetry reduced reaction free energy. The numerical results are compared with recent experiments of Doering and coworkers, confirming the accuracy of the most recent measurement on 2,4,6,7,9-pentamethyl-5-(5,5-$^2$H$_2$)methylene-11,11a-dihydro-12H-naphthacene as well as concerns about compromised accuracy, due to side reactions, of another measurement on 2-methyl-10-(10,10-$^2$H$_2$)methylenebicyclo[4.4.0]dec-1-ene.Comment: 14 pages, 8 figures, 6 table

The Changing Economics of Technological Learning

This paper deals with the emergence of new technologies of learning. In general, new tools and technologies of learning (simulation methods, electronic networks, etc.) ease some of the problems in the economics of learning. They help to reduce costs of information processing and to preserve technological diversity, as it is economically feasible to maintain alternative technology designs much longer. These effects in turn have a positive influence on the adaptive capacity of the techno-economic system. First, it enables to explore an entire spectrum of technological variety and thus to broaden the portfolio of technological alternatives. Second, it enables to produce both effective outputs and knowledge in the process of using a technology. This means that knowledge and information about environmental impacts of a technology can be continuously generated very early on

A comparison between detailed and configuration-averaged collisional-radiative codes applied to non-local thermal equilibrium plasma

A collisional-radiative model describing nonlocal-thermodynamic-equilibrium plasmas is developed. It is based on the HULLAC (Hebrew University Lawrence Livermore Atomic Code) suite for the transitions rates, in the zero-temperature radiation field hypothesis. Two variants of the model are presented: the first one is configuration averaged, while the second one is a detailed level version. Comparisons are made between them in the case of a carbon plasma; they show that the configuration-averaged code gives correct results for an electronic temperature Te=10 eV (or higher) but fails at lower temperatures such as Te=1 eV. The validity of the configuration-averaged approximation is discussed: the intuitive criterion requiring that the average configuration-energy dispersion must be less than the electron thermal energy turns out to be a necessary but far from sufficient condition. Another condition based on the resolution of a modified rate-equation system is proposed. Its efficiency is emphasized in the case of low-temperature plasmas. Finally, it is shown that near-threshold autoionization cascade processes may induce a severe failure of the configuration-average formalism.Comment: 9

Spin-Current Relaxation Time in Spin-Polarized Heisenberg Paramagnets

We study the spatial Fourier transform of the spin correlation function G_q(t) in paramagnetic quantum crystals by direct simulation of a 1d lattice of atoms interacting via a nearest-neighbor Heisenberg exchange Hamiltonian. Since it is not practical to diagonalize the s=1/2 exchange Hamiltonian for a lattice which is of sufficient size to study long-wavelength (hydrodynamic) fluctuations, we instead study the s -> infinity limit and treat each spin as a vector with a classical equation of motion. The simulations give a detailed picture of the correlation function G_q(t) and its time derivatives. At high polarization, there seems to be a hierarchy of frequency scales: the local exchange frequency, a wavelength-independent relaxation rate 1/tau that vanishes at large polarization P ->1, and a wavelength-dependent spin-wave frequency proportional to q^2. This suggests a form for the correlation function which modifies the spin diffusion coefficients obtained in a moments calculation by Cowan and Mullin, who used a standard Gaussian ansatz for the second derivative of the correlation function.Comment: 6 pages, 3 figure

Mn L2,3_{2,3} edge resonant x-ray scattering in manganites: Influence of the magnetic state

We present an analysis of the dependence of the resonant orbital order and magnetic scattering spectra on the spin configuration. We consider an arbitrary spin direction with respect to the local crystal field axis, thus lowering significantly the local symmetry. To evaluate the atomic scattering in this case, we generalized the Hannon-Trammel formula and implemented it inside the framework of atomic multiplet calculations in a crystal field. For an illustration, we calculate the magnetic and orbital scattering in the CE phase of \lsmo in the cases when the spins are aligned with the crystal lattice vector ${\vec a}$ (or equivalently ${\vec b}$) and when they are rotated in the $ab$-plane by 45$^{\circ}$ with respect to this axis. Magnetic spectra differ for the two cases. For the orbital scattering, we show that for the former configuration there is a non negligible $\sigma \to \sigma'$ ($\pi \to \pi'$) scattering component, which vanishes in the 45$^\circ$ case, while the $\sigma \to \pi'$ ($\pi \to \sigma'$) components are similar in the two cases. From the consideration of two 90$^\circ$ spin canted structures, we conclude there is a significant dependence of the orbital scattering spectra on the spin arrangement. Recent experiments detected a sudden decrease of the orbital scattering intensity upon increasing the temperature above the N\' eel temperature in \lsmo. We discuss this behavior considering the effect of different types of misorientations of the spins on the orbital scattering spectrum.Comment: 8 figures. In the revised version, we added a note, a reference, and a few minor changes in Figure 1 and the text. Accepted in Physical Review

Number skills and knowledge in children with specific language impairment.

The number skills of groups of 7- to 9-year-old children with specific language impairment (SLI) attending mainstream or special schools were compared with an age and nonverbal reasoning matched group (age control [AC]) and with a younger group matched on oral language comprehension. The SLI groups performed below the AC group on every skill. They also showed lower working memory functioning and had received lower levels of instruction. Nonverbal reasoning, working memory functioning, language comprehension, and instruction accounted for individual variation in number skills to differing extents depending on the skill. These factors did not explain the differences between SLI and AC groups on most skill

Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential

The mean field composite Fermion (CF) picture successfully predicts angular momenta of multiplets forming the lowest energy band in fractional quantum Hall (FQH) systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field, because these interactions have totally different energy scales. Rather, it results from the behavior of the Coulomb pseudopotential V(L) (pair energy as a function of pair angular momentum) in the lowest Landau level (LL). The class of short range repulsive pseudopotentials is defined that lead to short range Laughlin like correlations in many body systems and to which the CF model can be applied. These Laughlin correlations are described quantitatively using the formalism of fractional parentage. The discussion is illustrated with an analysis of the energy spectra obtained in numerical diagonalization of up to eleven electrons in the lowest and excited LL's. The qualitative difference in the behavior of V(L) is shown to sometimes invalidate the mean field CF picture when applied to higher LL's. For example, the nu=7/3 state is not a Laughlin nu=1/3 state in the first excited LL. The analysis of the involved pseudopotentials also explains the success or failure of the CF picture when applied to other systems of charged Fermions with Coulomb repulsion, such as the Laughlin quasiparticles in the FQH hierarchy or charged excitons in an electron-hole plasma.Comment: 27 pages, 23 figures, revised version (significant changes in text and figures), submitted to Phil. Mag.

The role of language in mathematical development; Evidence from children with specific language impairments.

A sample (n = 48) of eight-year-olds with specific language impairments is compared with age-matched (n = 55) and language matched controls (n = 55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised